Consider the following three linear equations graphed 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 graphed 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:
State the value of the y-intercept for following lines:
y = - 4 x + 1
y = 2
5 x = 4 y
x = 1
y = 3 x
Consider the following linear equations:
State the value of the gradient, m.
State the y-intercept, 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
Find the equations of the following lines:
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 - \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 whose gradient is 8 and goes through the point \left(0, - 4 \right).
A line that has the same gradient as y = 9 - 8 x and the same y-intercept as
y = - 5 x - 3.
A line has a gradient of - 3 and intercepts the y-axis at - 2.
Write 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.
Write the equation of the line in the form y = m x + c.
State whether the point \left( 8, - 31 \right) lies on this line.
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.
Consider the line graphed below:
State the the y-intercept.
State the gradient.
Consider the line graphed below:
State the y-intercept.
State the gradient.
Consider the line graphed on the number plane:
State the values of:
The gradient, m.
The y-intercept, c.
Write the equation of the line in gradient-intercept form.
Find the value of y when x = 27.
Consider the line graphed on the number plane:
State the values of:
The gradient, m.
The y-intercept, c.
Write the equation of the line in gradient-intercept form.
Find the value of y when x = 28.
State the value of the y-intercept.
By how much does the y-value increase as the x-value increases by 1?
Write the linear equation expressing the relationship between x and y.
Find the equations of the following lines in gradient-intercept form:
For each pair of points:
Find the gradient of the line that passes through the points.
Find the equation of the line.
\left(0, - 10 \right) and \left( - 8 , - 26 \right)
\left(0, -1\right) and \left(7, 27\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 line with equation y = \dfrac{8 - 5 x}{3}:
Express the line in the form y = m x + c.
Hence, what is the gradient, m, of the line?
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.
Express the following equations in general form.
y = 2 x - 3
y = \dfrac{2 x}{3} - 5
Consider the graph of the line:
What is the value of the y-intercept?
What is the gradient of the line?
Find the equation of the line in the form y = m x + c.
Express the equation of the line in general form ax + by + c = 0.
A straight line intercepts the y-axis at 5 and passes through the point \left( - 5 , 10\right).
Find the gradient of the line.
Express the equation of the line in general form, ax + by + c = 0.
A straight line passes through the point \left(0 ,\dfrac{3}{4}\right) with gradient 4.
Find the equation of the line in the form y = m x + c.
Express this equation in the general form a x + b y + c = 0.
Find the x-intercept.
A line has a gradient of - 5 and passes through the point \left( - 2 , - \dfrac{3}{8} \right).
By substituting into the equation y = m x + c, find the value of c for this line.
Express the equation of the line in general form, ax + by + c = 0.
A line has a gradient of \dfrac{5}{4} and passes through the point \left( - 9 , - 9 \right).
By substituting into the equation y = m x + c, find the value of c for this line.
Express the equation of the line in general form, ax + by + c = 0.