Consider the equation of a line y = mx + c.
Consider the following three linear equations with their graphs plotted on a number plane:
Equation 1: y = x + 1
Equation 2: y = 2 x + 1
Equation 3: y = 4 x + 1
What do all of the equations have in common?
What do all of the graphs have in common?
Describe all lines that have the form: y = m x + 1
Consider the following three linear equations with their graphs plotted on a number plane:
Equation 1: y = 2 x + 4
Equation 2: y = 2 x + 8
Equation 3: y = 2 x - 4
What do all of the equations have in common?
What do all of the graphs have in common.
Describe all lines that have the form: y = 2 x + c
Determine whether or not the gradients of the following pairs of equations are equal:
Consider the line plotted below:
State the the y-intercept.
State the gradient.
Consider the line plotted below:
By how much does the y-value change as the x-value increases by 1?
State the gradient of the line.
State whether or not the following lines have a y-intercept:
y = 2
5 x = 4 y
y = - 4 x + 1
x = 1
y = 3 x
Consider the following linear equations:
State the value of the gradient, m.
State the y-intecept, c.
y = - 2 x + 9
y = - 4 x - 8
y = 8 x + 6
y = - 1 - \dfrac{9 x}{2}
- 9 x + 9 y = 27
3 x - 10 y =- 2
Sketch the following lines on a number plane:
The line with a y-intercept of - 2 and gradient of - 3.
The line with a y-intercept of 3 and gradient of - \dfrac{3}{2}.
The line y = 2 x + 5.
The line y = \dfrac{1}{2} x - 1.
For each of the following equations:
Find the y-value of the y-intercept of the line.
Find the x-value of the x-intercept of the line.
Find the value of y when x = 3.
Sketch the line on a number plane.
For each of the following lines:
Find the y-coordinate of the y-intercept of the line.
Hence, write the equation of the line in gradient-intercept form.
Find the x-coordinate of the x-intercept of the line.
Sketch the line on a number plane.
A line has gradient \dfrac{4}{5} and passes through the point \left( - 10 , 4\right).
A line has gradient - 2 and passes through the point \left(3, - 8 \right).
A line has a gradient of - 3 and intercepts the y-axis at - 2.
Find the equation of the line in the form y = m x + c.
State whether the point \left( - 2 , 4 \right) lies on this line.
A line has a gradient of - 3 and cuts the y-axis at 8.
Find the equation of the line in the form y = m x + c.
State whether the point \left( 8, - 31 \right) lies on this line.
Find the equations of the following in the form y = mx + c :
A line that has the same gradient as y = 9 - 8 x and the same y-intercept as
y = - 5 x - 3.
A line whose gradient is 2 and crosses the y-axis at 5.
A line whose gradient is - 6 and crosses the y-axis at 9.
A line whose gradient is - 8 and crosses the y-axis at - 9.
A line whose gradient is - \dfrac{3}{4} and intercepts the y-axis at 3.
A line whose gradient is \dfrac{4}{3} and goes through the point \left(0, 3\right).
A line that has a gradient of - 2 and passes through \left( - 6 , - 3 \right)
A line whose gradient is 8 and goes through the point \left(0, - 4 \right).
A line whose gradient is 0 and goes through the point \left(0, \dfrac{2}{13}\right).
Consider the line plotted on the number plane.
State the values of:
The gradient, m.
The y-intercept, c.
Find the equation of the line in gradient-intercept form.
Find the value of y when x = 27.
Consider the line plotted on the number plane.
Find the equation of the line in gradient-intercept form.
Find the value of y when x = 50.
Consider the line plotted on the number plane.
Find the equation of the line in gradient-intercept form.
Find the value of y when x = 29.
Find the equations of the following lines in gradient-intercept form:
For the following lines passing through the given two points:
Hence, state the gradient of the line.
Find the equation of the line in the form y = m x + c.
\left(0, 2\right) and \left(2, 6\right)
\left(0, - 9 \right) and \left(5, 1\right)
\left(0, 2\right) and \left( - 7 , 44\right)
For each of the following linear equations:
Rewrite it in the form y = m x + c.
State the gradient of the line, m.
State the y-intercept of the line, c.
y = \dfrac{- 4 x + 16}{4}
9 x - y - 8 = 0.
y = 3 \left( 4 x - 3\right)
y = 6 \left( 3 x - 2\right)
3 x - 9 y - 27 = 0.
3 x - 4 y - 28 = 0
Consider the lines with the following equations:
Line A: 5 x + 3 y + 5 = 0
Line B: 7 x + 6 y - 3 = 0
Express the lines in the form y = m x + c.
State which line is steeper, A or B.
Determine which of the following lines are steeper: 2 x + 5 y - 5 = 0 or 4 x + 4 y + 1 = 0.
A straight line has gradient -1 and goes through the points \left(0, 2\right) and \left(a, - 6 \right).
Write the equation of the line in the form y = m x + b.
Find the value of a.
Determine whether the following statements about two parallel lines are true or false.
The y-value is changing at the same rate on both lines.
They intersect at one point.
They have the same value of c in y = m x + c.
They have the same value of m in y = m x + c.
They are equidistant from each other.
State whether the given pairs of lines are parallel:
y = - 2 x - 5 and y = - 2 x - 8
y = 7 x + 8 and y = - 5 x + 8
y = - 3 x - 2 and y = - 3 x + 9
y = - 6 x - 5 and y = - 6 x
Find the gradient of the following lines:
A line parallel to a line with gradient - 2.
Any line that is parallel to y = - 7 + 4 x.
State whether the following lines are parallel to y = 7 x + 3.
y = 7 x - 3
y = 6 x + 3
y = 7 x
y = - 7 x + 3
State whether the following lines are parallel to y = - 3 x + 2.
y = 3 x
y = - \dfrac{2 x}{3} + 8
- 3 y - x = 5
y = - 10 - 3 x