What does ' c ' represent in the gradient-intercept form of the equation of a straight line?

The ' c ' in the gradient-intercept form of the equation of a straight line represents the y -coordinate of the point at which the line intersects the y -axis ( y -intercept ).

Define parallel lines.

Parallel lines are lines that are always equidistant and never intersect .

What is the relationship between the gradients of parallel lines?

Parallel lines have the same gradient .

True or False? If two lines are parallel , their y -intercepts must be the same .

False. Parallel lines have the same gradient but can have different y -intercepts .

What is the gradient of a horizontal line?

The gradient of a horizontal line is 0 .

Define perpendicular lines.

Perpendicular lines are lines that intersect at right angles (90 degrees).

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Linear Functions & Graphs (DP IB Applications & Interpretation (AI))

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FrontEquations of a Straight Line
What is the formula for calculating the gradient of a straight line?
BackEquations of a Straight Line
The formula for calculating the gradient of a straight line is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Where:
$m$ is the gradient of the line
$(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are two different points on the line
This is given in your exam formula booklet.
FrontEquations of a Straight Line
State the point-gradient form of a straight line equation.
BackEquations of a Straight Line
The point-gradient form of a straight line equation is $(y - y_{1}) = m (x - x_{1})$
Where:
$m$ is the gradient of the line
$(x, y)$ are the coordinates of any point on the line
$(x_{1}, y_{1})$ are the coordinates of a specific point on the line
This is given in your exam formula booklet.

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What is the formula for calculating the gradient of a straight line?
The formula for calculating the gradient of a straight line is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Where:
- $m$ is the gradient of the line
- $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are two different points on the line
This is given in your exam formula booklet.
What does 'c' represent in the gradient-intercept form of the equation of a straight line?
The 'c' in the gradient-intercept form of the equation of a straight line represents the y-coordinate of the point at which the line intersects the y-axis (y-intercept).
State the point-gradient form of a straight line equation.
The point-gradient form of a straight line equation is $(y - y_{1}) = m (x - x_{1})$
Where:
- $m$ is the gradient of the line
- $(x, y)$ are the coordinates of any point on the line
- $(x_{1}, y_{1})$ are the coordinates of a specific point on the line
This is given in your exam formula booklet.
How can you find the x-intercept from the general form of a linear equation, $a x + b y + d = 0$ ?
The x-intercept from the general form of a linear equation, $a x + b y + d = 0$ is $(- \frac{d}{a}, 0)$ .
This comes from substituting in $y = 0$ and then solving for $x$ to get $x = - \frac{d}{a}$ .
Define parallel lines.
Parallel lines are lines that are always equidistant and never intersect.
What is the relationship between the gradients of parallel lines?
Parallel lines have the same gradient.
True or False?
If two lines are parallel, their y-intercepts must be the same.
False.
Parallel lines have the same gradient but can have different y-intercepts.
How can you determine if two lines are parallel using their equations?
Rearrange into $y = m x + c$ form and compare the coefficients of $x$ .
If they are equal, the lines are parallel.
What is the gradient of a horizontal line?
The gradient of a horizontal line is 0.
What is the equation of a vertical line?
The equation of a vertical line is $x = k$ , where $k$ is a constant.
E.g. $x = - 4$ is a vertical line that crosses the $x$ -axis at -4.
Define perpendicular lines.
Perpendicular lines are lines that intersect at right angles (90 degrees).
What is the relationship between the gradients of perpendicular lines?
The gradients of perpendicular lines are negative reciprocals of each other.
E.g. if a line, $l_{1}$ , has a gradient of -3, then a line, $l_{2}$ , that is perpendicular to $l_{1}$ will have a gradient of $\frac{1}{3}$ .

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