10.06 The point of intersection
For each of the following, state the coordinates of the point of intersection of the two lines:
The graph of y = 3 x - 4 is shown on the coordinate plane:
Consider the horizontal line with equation y = 8.
State the point of intersection of the graph of y = 3 x - 4 with the line y = 8.
Hence determine the value of x that solves the equation 3 x - 4 = 8.
The graph of y = -2 x - 4 is shown on the coordinate plane:
State the point of intersection of the graph with the line y = - 12.
Hence determine the value of x that solves the equation - 2 x - 4 = - 12.
The graph of y = -\dfrac{x}{2} + 6 is shown on the coordinate plane:
In order to solve the equation \\- \dfrac{x}{2} + 6 = 8, state the equation of the other line that must be graphed on the axes.
Hence find the solution to - \dfrac{x}{2} + 6 = 8.
Explain why it is not necessary to write the y-value in your answer to part (b).
The graph of y = \dfrac{4x}{3} + 5 is shown on the coordinate plane:
In order to solve the equation \\ \dfrac{4x}{3} + 5 = 13, state the equation of the other line that must be graphed on the axes.
Hence find the solution to \dfrac{4 x}{3} + 5 = 13.
Emma wishes to find the point of intersection of the following lines:
y = -2 x + 3 \\ y = -1Complete the table of values for \\y = -2 x + 3:
| x | -1 | 0 | 1 |
|---|---|---|---|
| y |
Sketch the graphs of both lines on a coordinate plane.
Hence determine the point of intersection.
Scott wishes to find the point of intersection of the following lines:
y = 2 x + 1 \\ y = -3 x + 11Complete the table of values for \\y = 2 x + 1:
| x | -1 | 0 | 1 |
|---|---|---|---|
| y |
Complete the table of values for \\y = -3 x + 11:
| x | -1 | 0 | 1 |
|---|---|---|---|
| y |
Sketch the graphs of both lines on a coordinate plane.
Hence determine the point of intersection.
For each of the following pairs of equations:
Sketch the graph of the two lines on the same coordinate plane.
Find the coordinates of the point of intersection.
y = 3
x = - 3
y = 2 x + 2
x = - 3
y = 3 x - 4
y = 5
y = - 2 x + 4
y = 8
y = 3 x + 3
x = - 1
y = x + 3
y = 3 x - 5
y = - x + 6
y = x + 2
y = - x + 2
y = 2 x - 4
y = - 4 x + 2
y = 3 x - 12
y = \dfrac{x}{2} + 3
y = 3 x - 2
y = \dfrac{x}{2} - 2
y = - 2 x + 3
y = 5 x + 6
y = 2 x + 12
y = 3 x - 3
y = - 4 x + 11
y = x - 9
y = - x - 7
y = 2 x - 7
y = - \dfrac{x}{2} - 2
y = \dfrac{x}{2} + 5
y = 3 x