Answer:
y = -4x - 1
Step-by-step explanation:
Let's first find the equation of the line segment AB. The equation of a line in slope-intercept form is y = mx + b where m represents the slope and b represents the y-intercept. Start by finding the slope.
The equation for slope is: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. These variables represent any pair of coordinates on the line. In this case since the two points chosen are A and B, thus:
[tex]x_2=-2\\x_1=3\\y_2=15\\y_1=-5[/tex]
If we plug these values into the equation, we get:
[tex]\frac{15-(-5)}{-2-3}=\frac{20}{-5}=-4[/tex]
Now we need to find the equation of a line that passes through the point (-1, 3) and is parallel to AB. If two lines are parallel they share the same slope. The equation of the line parallel to AB is y = -4x + b. We can plug in the coordinate (-1, 3) into the equation to solve for b.
[tex]y = mx+b\\3 = -4(-1) +b\\3=4+b\\\text{Subtract 4 from both sides}\\b=-1[/tex]
Therefore the equation of the line that passes through the point (-1, 3) and is parallel to AB is y = -4x - 1.
