Question

use the drawing tools to form the correct answer on the graph. graph the line that represents this equation: y + 2 = \frac{3}{4}(x + 3)

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 2=\frac{3}{4}(x + 3) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( m=\frac{3}{4} \) and the point \( (x_1,y_1)=(- 3,-2) \).

Step2: Find two points on the line

• First, use the point we identified from the point - slope form. When \( x=-3 \), \( y=-2 \), so the point \( (-3,-2) \) is on the line.
• Second, to find another point, we can use the slope. The slope \( m = \frac{3}{4}\) means that for a run (change in \( x \)) of 4 units, the rise (change in \( y \)) is 3 units. Starting from the point \( (-3,-2) \), if we add 4 to \( x \) (i.e., \( x=-3 + 4=1 \)) and add 3 to \( y \) (i.e., \( y=-2+3 = 1 \)), we get the point \( (1,1) \).

Step3: Plot the points and draw the line

Plot the points \( (-3,-2) \) and \( (1,1) \) on the coordinate plane. Then, use a straight - edge to draw a line passing through these two points. The line should extend in both directions to represent the linear equation.

Answer:

To graph the line \( y + 2=\frac{3}{4}(x + 3) \), plot the points \((-3,-2)\) and \((1,1)\) (found using the point - slope form and the slope) and draw a straight line through them.