Chapter 5.4, Problem 4STP

For Exercises $1-5,$ choose the correct letter.

Which equation represents the line shown in the graph? $y=-3x-2$

G. $y=3x+2$

H. $y+4=-3(x-2)$

I. $y+8=-3(x-2)$

To determine

To write the equation represents the line shown in the graph and choose the correct option.

Answer to Problem 4STP

  $\text{H}\text{. }y+4=-3\left(x-2\right)$

Explanation of Solution

Given information:

A graph of line as

Solution:

From the graph, it can be seen that the line crosses at the y -axis at (0, 2)

So, the y -intercept ( b ) = 2.

Go 6 units downward and 1 unit right then to get a point (2, -4)

Therefore, the slope = $\frac{Rise}{Run}=\frac{-4-2}{2-0}=\frac{-6}{2}=-3$

So, the slope ( m ) of line is $-3.$

Then plug the value of slope (m) and coordinates (2, -4) in point slope form.

Point slope form: $\left(y-y_1\right)=m\left(x-x_1\right)$

  $y-\left(-4\right)=\left(-3\right)\left(x-2\right)$

Simplify:

  $y+4=-3\left(x-2\right)$

Therefore, the equation of given graph of line is $y+4=-3\left(x-2\right).$