Consider the line through Point A\left(0, 4\right) and Point B\left(1, 0\right).
Find the rise (change in the y-value) going from point A to point B.
Find the run (change in x-value) going from point A to point B.
Find the gradient of the interval AB.
Find the gradient of the line that passes through Point A \left(2, - 6 \right) and the origin.
Find the gradient of the line going through A and B.
For the following equations:
State the gradient.
State the y-intercept.
y = - 2 x
y = 1 + 10 x
y = - 1 - \dfrac{9 x}{2}
For the following equations:
Rewrite the equations in gradient-intercept form.
State the gradient.
State the y-intercept.
y = 6 \left( 3 x - 2\right)
y = \dfrac {8 x + 12}{2}
5 x - 30 y - 25 = 0
A line passing through the points \left( - 1 , 4\right) and \left( - 4 , t\right) has a gradient of - 3.
Find the value of t.
Consider the points A\left(24, - 56 \right), B\left( - 6 , - 2 \right) and C\left( - 11 , 7\right).
Find the gradient of AB.
Find the gradient of BC.
Do the points A, B, and C lie on a straight line?
A straight line with gradient 1 passes through point A(-4, 2). What is the gradient between A and any other point on the line?
The point \left( - 5 , 7\right) lies on the line a x - 5 y + 10 = 0.
Find the value of a.
Find the gradient of the line.
Consider the following straight line graph:
What is the slope of the line?
What is the y-intercept of the line?
Does this line have an x-intercept?
Find the equation of the following lines in gradient-intercept form:
A line whose gradient is - 8 and crosses the y-axis at - 9.
A line that passes through the point A\left( - 4 , 3\right) and has a gradient of - 9.
A line that goes through \left(0, \dfrac{2}{13}\right) and has a gradient of 0.
Express the following equations in general form:
y = 2 x - 3
y = \dfrac {2 x}{3} + 3
A line has gradient 3 and passes through the point \left(7, \dfrac{2}{13}\right).
By substituting into the equation y = m x + c, find the value of c.
Write the equation of the line in general form.
A line passes through the points \left(4, - 6 \right) and \left(6, - 9 \right).
Find the gradient of the line.
Write the equation of the line in gradient-intercept form.
A line passes through the points \left(0, 4\right) and \left( - 6 , - 50 \right).
What is the gradient of the line?
Write the equation of the line in gradient-intercept form.
A line has an x-intercept of - 2 and a y-intercept of 7. Write the equation of the line in general form.
Consider the line with equation 2 x + y - 8 = 0.
Find the x-intercept of the line.
Find the equation of a line with a gradient of - 4 that passes through the x-intercept of 2 x + y - 8 = 0.
Find the equation of the horizontal line passing through the point \left(8, - 4 \right).
Find the equation of a line that has the same gradient as y = 7 - 3 x and the same y-intercept as y = - 7 x - 8.
Consider the graph below:
What is the y-intercept of the line?
What is the gradient of the line?
Find the equation of the line in the form:
Every point on a line is shifted 3 units down, resulting in the line with equation y = 3 x + 1.
What was the equation of the original line?
State the equation of the graphed line:
Consider the equation y = - x - 2.
Complete the table of values for this equation.
| x | -1 | 0 | 1 |
|---|---|---|---|
| y |
Sketch the graph of the line.
What are the coordinates of the y-intercept?
What are the coordinates of the x-intercept?
What is the y value when x = 3?
What is the x value when y = - 4?
Consider the equation y = - x + 1.
Complete the table of values for this equation:
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
Sketch the graph of the line.
Determine whether the point (1.5, -0.5) lies on the line.
For the following equations:
Find the y-intercept.
Find the x-intercept.
Sketch the graph of the line.
Graph the following lines:
y = - 3
x = - 6
y = - 4 x
y = - x + 4
y = 4 x - 1
6 x - 3 y + 18 = 0
Graph the line that has an x-intercept of - 8 and a gradient of - 1.
Consider the following table of values:
| x | -4 | -2 | 0 | 2 |
|---|---|---|---|---|
| y | -2 | -2 | -2 | -2 |
Graph the line going through these points.
Write the equation of the line that goes through these points.
A line has a gradient of - \dfrac{2}{3} and passes through the point \left( - 3 , 4\right).
By substituting into the equation y = m x + c, find the value of c.
Hence, write the equation of the line in gradient-intercept form.
Find the x-intercept of the line.
Sketch the graph of the line.
The function f \left( x \right) is defined below:
f\left(x\right) = \begin{cases} x+2, & \text{when}\ x\geq 5 \\ x-4, & \text{when}\ x\lt 5\\ \end{cases}Sketch the graph of the function.
What is the domain of f \left( x \right)?
What is the range of f \left( x \right)?
What is the gradient of any line parallel to the x-axis?
What is the equation of the line that passes through the point (9, 4) and is parallel to the y-axis?
State whether the following lines are parallel to the line with equation y = 9 x + 2:
y = 9 x
y = 5 x + 5
y = 9 x + 5
y = - 9 x + 2
y = 9 x - 2
y = 5 x + 2
Consider the pair of lines:
-
Line 1: 0 = - 3 y - 5 x + 6
Line 2: y = ax -1
If line 1 is parallel to line 2, find the value of a.
Find the equations of two lines that are both parallel to x = - 2, and 4 units away from the line x = - 2.
Consider the pair of lines:
Line 1: - x + 4 y + 2 = 0
Line 2: d x + 12 y + 6 = 0
Find the gradient of Line 1.
Find the gradient of Line 2.
Given that the two lines are parallel, find the value of d.
Consider a line with equation: 5 x - 4 y + 2 = 0.
Find the gradient of a new line that is parallel to 5 x - 4 y + 2 = 0.
Find the equation of this new line given that it passes through point \left( - 4 , 6\right). Express the equation in general form.
What is the gradient of any line perpendicular to y = 4 x - 9?
Find the equation of a line that is perpendicular to y = - \dfrac {3 x}{4} + 7, and passes through the point \left(0, 6\right).
A line is perpendicular to the interval joining B\left(4, - 5 \right) and C\left( - 7 , 4\right).
Find m, the gradient of the line.
Find the equation of the line if it passes through \left(7, - 1 \right).
Given that Line A: y = \left(t + 7\right) x - 1 and Line B: y = \dfrac {x}{4} - 4 are perpendicular, find the value of t.
Consider the line 5 x - 3 y - 9 = 0.
Find the y-intercept of the line.
Find the equation of the line that is perpendicular to the given line and has the same y-intercept. Write the equation of the line in general form.
A staircase is to be built so that its maximum steepness (gradient) is 0.6. If each step goes in by 22 centimetres, what is the maximum height in centimetres it can rise vertically?
State whether the following points line on the line y - 5 = 3 \left(x + 4\right):
\left( - 5 , 4\right)
\left( - 4 , 5\right)
\left( - 2 , 8\right)
\left(-1, 14\right)
Write the equations of the following functions in piecewise form: