The equation of a line is .
For the line find:
A new line, intersects the -axis at (4, 0) and is perpendicular to .
Find:
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The equation of a line is .
For the line find:
A new line, intersects the -axis at (4, 0) and is perpendicular to .
Find:
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The coordinates of point are and the coordinates of point B are . is the midpoint of .
Find the coordinates of .
The line passes through and .
Find the gradient of .
Find the equation of the line Give your answer in the form , where and are integers.
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The coordinates of point are and the coordinates of point are . is the midpoint of .
Find the coordinates of .
The line passes through the points and .
Find the equation of . Give your answer in the form of .
A new line, , is the perpendicular bisector to .
Find the equation of . Give your answer in the form of .
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Plumber A charges a fixed fee of $25 plus $15 per hour.
Using for the number of hours a job takes, and for the total cost of a job, in dollars, from Plumber A, write down an equation connecting and .
A job takes the plumber seven hours.
Calculate the total cost of the job.
Plumber B charges a fixed fee of $20 plus $16 per hour.
Using for the number of hours a job takes, and for the total cost of a job, in dollars, from Plumber B, write down an equation connecting and .
Determine which plumber would be the cheapest for a job taking six.
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The diagram below shows the line , which intersects the -axis at A and the -axis at B.
Find the equation of Give your answer in the form of .
Find the length of [AB].
A second line, is parallel to and intersects the -axis at C.
Find the equation of Give your answer in the form , where and are integers.
Find the coordinates where intersects the -axis.
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Photocopy shop A charges $122 for 115 copies, and $190 for 200 copies.
Assuming a linear relationship, find
Photocopy shop B charges $0.82 per copy and a fixed fee of $25.50.
State which photocopy shop is cheaper to make 220 copies.
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A family can be supplied with electricity by two companies that have different pricing structures:
Company A: Fixed fee of $25/month and $0.2 per kWh consumed.
Company B: Fixed fee of $10/month and $0.22 per kWh consumed.
Determine the equation of the cost function for both companies, where the total monthly cost is a function of the monthly electricity consumption in kWh.
Calculate the monthly energy consumption that results in the same monthly cost from both companies.
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Ardie’s monthly expenditure, is a linear function of his monthly income, . Ardie’s monthly expenditure is $1000 when his monthly income is $1200 and his monthly expenditure increases by $60 for every $150 increase in his monthly income.
Write an expression connecting Ardie’s monthly expenditure, with his monthly income, .
Calculate Ardie’s monthly expenditure when his monthly income is $1885. Give your answer to the nearest dollar.
Find Ardie’s monthly income when his monthly expenditure is $1070. Give your answer to the nearest dollar.
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The diagram below represents a mountain with a west facing slope and an east facing slope labelled and respectively.
Horizontal scale: 1 unit represents 100 m.
Vertical scale: 1 unit represents 100 m.
Find the gradient of the west facing slope.
The gradient of the east facing slope in the diagram is .
Find the total distance to hike over the mountain in km.
Suggest a reason as to why the actual total distance hiked may be greater than the distance found in part (b).
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The straight lines and are shown in the diagram below intercepts the -axis at and the -axis at and intercepts the -axis at and the -axis at .
Giving your answer in the form , find:
Find the area of the shaded region.
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A line passing through the origin , is perpendicular to a line with equation
The two lines meet at point . is a point such that OP : PR = 3 : 1.
Find the equation of the perpendicular line and hence, the co-ordinates of point R.
Find the coordinates of P.
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The diagram below shows the line with the equation .
Point P has coordinates point Q has coordinates and point R has coordinates . M is the midpoint of [PQ].
Write down the coordinates of M.
Show that Q lies on .
Show that R lies on
Find the area of PQR.
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The line passes through the points and .
Find the equation of Give your answer in the form of .
A new line, , is perpendicular to and passes through the point .
Find the equation of . Give your answer in the form of .
The point is the intersection of and .
Find the coordinates of .
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Point A has coordinates and point B has coordinates . M is the midpoint of and has coordinates .
Find the value of x and y.
The line passes through A and B.
Find the equation of . Give your answer in the form where and are integers.
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The line passes through and .
Find the equation of . Give your answer in the form .
Point C is such that B is the midpoint of .
Find the coordinates of C.
Point D is such that C is the midpoint of .
Find the coordinates of D.
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Point A has coordinates and point B has coordinates . The line passes through M, the midpoint of . The gradient of is 2.
Write down the equation of , giving your answer in the form .
The line passes through A and has a gradient of 5.
Write down the equation of , giving your answer in the form .
Point C is the intersection of and .
Write down the coordinates of C, giving the and coordinates as fractions.
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Finn borrows $3200 from his parents and decides to pay them back $ in the first month and then $ each subsequent month.
After two months Finn has paid back his parents a total of $1000, this can be expressed as . After half a year he still owes his parents $1000.
Write down another equation connecting m and c.
Find the value of m and c.
Finn’s parents apply a 6.25% net interest to the $3200 total.
Calculate the number of months it takes Finn to pay back his parents.
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The line has the equation . Point A has coordinates and is the intersection of and is perpendicular to .
Write down the equation of , giving your answer in the form
Point B lies on and is positioned such that AB is 12 units and the -coordinate for B is less than the -coordinate for A.
Find the coordinates of B.
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The points K and N lie on the line where , .
KN has a length of 5 units.
Find all the possible values for and .
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Point A has coordinates , point B has coordinates , and point C has coordinates (8, 1).
Calculate the length of AC.
Point D lies on the line . The line is perpendicular to the line (AC).
Find the coordinates of D.
Calculate the area of the triangle ABC.
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The distance between points P and Q is equal to 25 units.
Find the possible values of .
It is given that
Point R is such that point Q is the midpoint of the line segment with endpoints P and R.
Write down the coordinates of R.
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A cat breeder is measuring the rate at which a kitten grows by measuring its “back-length”, which is the distance from the base of the neck to the base of the tail.
At 1 week old the kitten measured 2.42 cm. 8 weeks later the kitten’s back length had doubled.
Using a linear model, find an equation linking , the kitten’s “back-length” in centimetres, to , the age of the kitten in weeks.
Find the kitten’s “back-length” at birth.
Use the model to find the age, in weeks, of the kitten that has a “back-length” of 7 cm.
This breed of cat is fully grown after 50 weeks.
Find the cat’s “back-length” at 50 weeks.
Comment on the suitability of the linear model used.
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Point P has coordinates , R has coordinates . The equation of the line PQ is and the equation of the line QR is .
Find the coordinates of point Q.
Find the distance of PQ and QR.
Find the area of triangle PQR.
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Point P has coordinates (4, 2) and point Q has coordinates (1, 8). is the perpendicular bisector of [PQ].
Find the equation of , giving your answer in the form .
passes through Q and has a gradient of 3.
Find the equation of , giving your answer in the form .
Point C lies on and has a negative coordinate. The length of QC is 14 units.
Find the coordinates of C.
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Point A has coordinates , passes through points A and B and has the equation The length of [AB] is 10 units.
Find the possible coordinates of point B.
passes through points C and D, is parallel to and crosses the -axis when .
Write down the equation of . Give your answer in the form , where and are integers.
Point C has coordinates and CD is half the length of AB.
Find the possible coordinates of point D.
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The line passes through A and B
Find the equation of . Give your answer in the form , where and are integers.
.
The line passes through M, the midpoint of [AB] and has a gradient of 7.
Find the equation of . Give your answer in the form , where and are integers.
Point C lies on such that MC has a length of 12 units.
Find the possible coordinates of C.
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Carpenter A charges a fixed fee of $28 plus $22.50 per hour. The carpenter then charges tax on top of the total cost of 21%.
Defining suitable variables, write down an equation to represent the charges, including tax, made by the carpenter.
Carpenter B charges a fixed fee of $35 and $26.50 per hour. These prices already account for tax.
Find the number of hours for which both carpenters charge the same amount.
Tom needs a job doing by a carpenter that he estimates will take 8.5 hours. Carpenter C has given Tom a fixed quote of $250.
Determine which carpenter would be the cheapest option for Tom.
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The line has equation and crosses the -axis at point A.
Find the value of .
The line is perpendicular to and crosses the -axis at B.
Write down the equation of . Give your answer in the form , where and are integers.
crosses the -axis at point C.
Find the area of the triangle OAC, where O is the origin. Give your answer as a fraction.
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The points A and B lie on the line where AB has a length of 13 units.
Find all the possible and values.
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A quadrilateral has four vertices with coordinates .
Show that [AB] and [CD] are parallel.
Calculate the distance of
Find the area of the quadrilateral .
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The point lies on the line crosses the -axis at point .
Another line, , is perpendicular to at the point F and crosses the -axis at the point .
Find the area of the triangle . Give your answer as a fraction.
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