Question

use technology to find points and graph the line $2y = -3x + 8$, following the instructions below.
done plotting points
plot at least two points that fit on the axes below. click a point to delete it.
(coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines present)

Explanation:

Step1: Rewrite the equation in slope - intercept form

The given equation is \(2y=-3x + 8\). We can rewrite it in the form \(y=mx + b\) (slope - intercept form) by dividing both sides of the equation by 2.
\(y=\frac{-3x + 8}{2}=-\frac{3}{2}x+4\)

Step2: Find the y - intercept point

The y - intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation \(y=-\frac{3}{2}x + 4\).
\(y=-\frac{3}{2}(0)+4=4\). So one point on the line is \((0,4)\).

Step3: Find another point

Let's find the x - intercept. The x - intercept occurs when \(y = 0\). Substitute \(y = 0\) into the equation \(y=-\frac{3}{2}x + 4\).
\(0=-\frac{3}{2}x+4\)
Add \(\frac{3}{2}x\) to both sides: \(\frac{3}{2}x = 4\)
Multiply both sides by \(\frac{2}{3}\): \(x=\frac{8}{3}\approx2.67\). But we can also choose a convenient value for \(x\), for example, let \(x = 2\).
Substitute \(x = 2\) into \(y=-\frac{3}{2}x + 4\): \(y=-\frac{3}{2}(2)+4=-3 + 4=1\). So another point on the line is \((2,1)\). We can also use \(x = 2\) gives \(y = 1\), \(x=4\) gives \(y=-\frac{3}{2}(4)+4=-6 + 4=-2\), etc. But for graphing, two points like \((0,4)\) and \((2,1)\) (or \((0,4)\) and \((\frac{8}{3},0)\)) can be used.

Answer:

Two points on the line \(2y=-3x + 8\) are \((0,4)\) and \((2,1)\) (other valid points can also be used, e.g., \((\frac{8}{3},0)\) and \((0,4)\)). To graph the line, plot the points \((0,4)\) and \((2,1)\) (or other pairs of points found) and draw a straight line through them.