Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
First off, let's write the line in point-slope form:
[tex]\rm \hookrightarrow (y-y_0)=m(x-x_0)[/tex]
- (x₀, y₀) any random point on the line
- 'm' is the value of the slope
Let's calculate the slope:
[tex]\rm \hookrightarrow Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
- (x₁, y₁): any random point on the line ⇒ (-2, -6)
- (x₂,y₂): any random point on the line that is not (x₁, y₁) ⇒ (2, -3)
[tex]\rm \hookrightarrow slope = \frac{-3--6}{2--2} =\frac{3}{4}[/tex]
Now that we found the slope, let's put it into the point-slope form
⇒ we need (x₀, y₀) ⇒ let's use (2,-3)
[tex](y-(-3))=\frac{3}{4} (x-2)\\y+3=\frac{3}{4} (x-2)[/tex]
The equation, however, could also be put into 'slope-intercept form'
⇒ gotten by isolating the 'y' variable to the left
[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex]
Answer:[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex] or [tex]y+3=\frac{3}{4} (x-2)[/tex]
*Either equations work, put the one that you are the most familiar with
Hope that helps!
#LearnwithBrainly
