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
It costs Buzz \$6.00 per month to operate his existing incandescent light bulbs in his home. He has two options moving forward:
Option 1 - Incandescent: Stay with the incandescent bulbs at \$6.00 per month.
Option 2 - Fluorescent : Buy new energy efficient fluorescent bulbs for \$8.00 which cost \$2.00 per month after they are installed.
The graph shows the cost per month of option 1.
On the same graph, plot the relationship for the cost per month of option 2.
After how many months would the two options cost the same?
After 6 months, which option is cheaper and by how much?
A rectangular zone is to be 3 \text{ m} longer than it is wide, with a total perimeter of 18 \text{ m}.
Let y represent the length of the rectangle and x represent the width. Construct two equations that represent this information.
Sketch the two lines on the same number plane.
Hence, find the length and width of the rectangle.
A band plans to record a demo at a local studio. The cost of renting studio A is \$250 plus \$50 per hour. The cost of renting studio B is \$50 plus \$100 per hour. The cost, y, in dollars of renting the studios for x hours can be modelled by the linear system:
Studio A: y = 50 x + 250
Studio B: y = 100 x + 50
Sketch the two lines on the same number plane.
State the coordinate which satisfies both equations.
What does the coordinate from part (d) mean?
Michael plans to start taking an aerobics class. Non-members pay \$4 per class. Members pay a \$10 one-time fee, but only have to pay \$2 per class. The monthly cost, y, of taking x classes can be modelled by the linear system:
Non-members: y = 4 x
Members: y = 2 x + 10
Sketch the two lines on the same number plane.
State the coordinate which satisfies both equations.
What does the coordinate from part (b) mean?
The cost of manufacturing toys, C, is related to the number of toys produced, n, by the formula C = 400 + 2 n. The revenue, R, made from selling n toys is given by R = 4 n.
Sketch the graphs of cost and revenue on the same number plane.
How many toys need to be produced for the revenue to equal the cost?
State the meaning of the y-coordinate of the point of intersection.
Given the cost function C \left( x \right) = 0.4 x + 2015 and the revenue function R \left( x \right) = 3 x, find the coordinates of the point of intersection, or the break-even point.
The two equations y = 3 x + 35 and y = 4 x represent Laura’s living expenses and income from work respectively.
Find the point of intersection of the two equations.
Sketch both equations on the same number plane.
State the meaning of the point of intersection of the two lines.
The two equations y = 4 x + 400 and y = 6 x represent a company's revenue and expenditure respectively.
Find the point of intersection of the two equations.
Sketch both equations on the same number plane.
State the meaning of the point of intersection of the two lines.