Question

an equation is shown.
$y = -\frac{2}{3}x + 7$
use the line tool to graph the equation.
note: only use two points to graph the equation. any additional points used will be scored incorrectly.
(graph with y-axis labeled from -2 to 9, x-axis labeled from -9 to 9, and a grid. buttons: move, delete, line, clear all)

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{2}{3}x + 7\), when \(x = 0\), \(y=-\frac{2}{3}(0)+7=7\). So one point is \((0,7)\).

Step2: Find another point

We can choose a value of \(x\) that makes the calculation easy. Let's take \(x = 3\) (because the denominator of the slope is 3). Substitute \(x = 3\) into the equation: \(y=-\frac{2}{3}(3)+7=- 2 + 7 = 5\). So another point is \((3,5)\). We can also check with \(x = 6\): \(y=-\frac{2}{3}(6)+7=-4 + 7 = 3\), point \((6,3)\) or \(x=-3\): \(y=-\frac{2}{3}(-3)+7 = 2 + 7=9\), point \((-3,9)\). We can use two of these points (e.g., \((0,7)\) and \((3,5)\)) to graph the line.
To graph the line, plot the two points (e.g., \((0,7)\) and \((3,5)\)) on the coordinate plane and then use the line tool to draw a line through them.

Answer:

To graph \(y =-\frac{2}{3}x + 7\), plot the points \((0,7)\) (y - intercept) and another point (e.g., \((3,5)\) or \((6,3)\) or \((-3,9)\)) and draw a line through them. For example, using \((0,7)\) and \((3,5)\):

• Plot \((0,7)\) (on the y - axis, 7 units up from the origin).
• Plot \((3,5)\) (3 units to the right on the x - axis and 5 units up on the y - axis).
• Use the line tool to connect these two points.