Question

1. $y = -\frac{3}{2}x + 2$

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{3}{2}x + 2\), the y - intercept \(b = 2\). So the line crosses the y - axis at \((0,2)\).

Step2: Use the slope to find another point

The slope \(m=-\frac{3}{2}\), which means for a run (change in \(x\)) of \(2\), the rise (change in \(y\)) is \(- 3\). Starting from \((0,2)\), if we move \(2\) units to the right (increase \(x\) by \(2\)) and \(3\) units down (decrease \(y\) by \(3\)), we get the point \((0 + 2,2-3)=(2,-1)\).

Step3: Plot the points and draw the line

Plot the points \((0,2)\) and \((2, - 1)\) on the coordinate plane and then draw a straight line through them.

(If we were to just describe the graphing process, these are the key steps. The actual graphing would involve marking these points on the given grid and connecting them.)

Answer:

To graph \(y =-\frac{3}{2}x + 2\), plot the y - intercept \((0,2)\) and use the slope \(-\frac{3}{2}\) to find another point (e.g., \((2,-1)\)) and draw a line through these points.