Question

use the drawing tools to form the correct answer on the graph.
graph the line that represents this equation:
y + 2 = \frac{3}{5}(x + 3)

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 2=\frac{3}{5}(x + 3) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-3,-2) \) and the slope \( m = \frac{3}{5} \).

Step2: Plot the point

First, we plot the point \( (-3,-2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{3}{5} \) means that for a run of 5 units (increase in \( x \) by 5), the rise is 3 units (increase in \( y \) by 3). Starting from the point \( (-3,-2) \), if we add 5 to the \( x \) - coordinate (\( - 3+5 = 2 \)) and add 3 to the \( y \) - coordinate (\( -2 + 3=1 \)), we get the point \( (2,1) \).

Step4: Draw the line

Draw a straight line passing through the points \( (-3,-2) \) and \( (2,1) \).

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \((-3,-2)\) with a slope of \(\frac{3}{5}\) (also passing through \((2,1)\) as calculated). If we were to describe the key points: one point is \((-3,-2)\) and another is \((2,1)\), and the line connecting them.)

Answer:

Step1: Identify the form of the equation

The given equation is \( y + 2=\frac{3}{5}(x + 3) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-3,-2) \) and the slope \( m = \frac{3}{5} \).

Step2: Plot the point

First, we plot the point \( (-3,-2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{3}{5} \) means that for a run of 5 units (increase in \( x \) by 5), the rise is 3 units (increase in \( y \) by 3). Starting from the point \( (-3,-2) \), if we add 5 to the \( x \) - coordinate (\( - 3+5 = 2 \)) and add 3 to the \( y \) - coordinate (\( -2 + 3=1 \)), we get the point \( (2,1) \).

Step4: Draw the line

Draw a straight line passing through the points \( (-3,-2) \) and \( (2,1) \).

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \((-3,-2)\) with a slope of \(\frac{3}{5}\) (also passing through \((2,1)\) as calculated). If we were to describe the key points: one point is \((-3,-2)\) and another is \((2,1)\), and the line connecting them.)