Question

1. equations of two lines are given:

\\(y = 3x - 1\\)
\\(y = -2x + 9\\)

a) graph both lines on the grid to the right.

b) what are the coordinates of the point of intersection?

Explanation:

Identify key features of the first line

Using the Slope-Intercept Form knowledge point:
The first equation is \(y = 3x - 1\).
The \(y\)-intercept is \((0, -1)\).
The slope is \(m = 3\).
A second point on this line is \((2, 5)\).

Identify key features of the second line

Using the Slope-Intercept Form knowledge point:
The second equation is \(y = -2x + 9\).
The \(y\)-intercept is \((0, 9)\).
The slope is \(m = -2\).
A second point on this line is \((2, 5)\).

Solve for the intersection point algebraically

Set the two equations equal to each other:

$$3x - 1 = -2x + 9$$

Add \(2x\) to both sides:

$$5x - 1 = 9$$

Add \(1\) to both sides:

$$5x = 10$$

Divide by \(5\):

$$x = 2$$

Substitute \(x = 2\) back into the first equation:

$$y = 3(2) - 1 = 5$$

The intersection point is \((2, 5)\).

Answer:

Question 5a

To graph the lines on the grid:

• For \(y = 3x - 1\), plot the \(y\)-intercept at \((0, -1)\) and use the slope of \(3\) to plot another point at \((2, 5)\), then draw a straight line through them.
• For \(y = -2x + 9\), plot the \(y\)-intercept at \((0, 9)\) and use the slope of \(-2\) to plot another point at \((2, 5)\), then draw a straight line through them.

Question 5b

The coordinates of the point of intersection are \((2, 5)\).