Answer:
part 1) The equation of the line in point slope form is [tex]y+5=-3(x-1)[/tex]
Part 2) The equation in slope intercept form is [tex]y=-3x-2[/tex]
Explanation:
Part 1) Write an equation for the line in point-slope form
we have the points
(1, –5) and (–3, 7)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{7+5}{-3-1}[/tex]
[tex]m=\frac{12}{-4}[/tex]
[tex]m=-3[/tex]
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-3[/tex]
[tex]point\ (1,-5)[/tex]
substitute
[tex]y+5=-3(x-1)[/tex] ----> equation of the line in point slope form
Part 2) Rewrite the equation in slope-intercept form.
[tex]y=mx+b[/tex]
we have
[tex]y+5=-3(x-1)[/tex]
Convert to slope intercept form
Isolate the variable y
Distribute right side
[tex]y+5=-3x+3[/tex]
Subtract 5 both sides
[tex]y=-3x+3-5[/tex]
[tex]y=-3x-2[/tex]
