Answer: [tex]y=-1.5x[/tex]
Step-by-step explanation:
The Slope-Intercept form of the equation of the line is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Find the slope of this line using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
You can say that:
[tex]y_2=-6\\y_1=3\\x_2=4\\x_1=-2[/tex]
Substituiting values, you get:
[tex]m=\frac{-6-3}{4-(-2)}\\\\m=-1.5[/tex]
Now, you must substitute the slope and any point of the line, into [tex]y=mx+b[/tex] and then you must solve for "b" in order to find its value. You get that this is:
[tex]3=-1.5(-2)+b\\\\3=3+b\\\\3-3=b\\\\b=0[/tex]
Since the y-intercept is 0, the line passes through the origin. Therefore, you get that the equation of this line in Slope-Intercept form, is:
[tex]y=-1.5x[/tex]
