Answer:
part 1) The equation of the line in point slope form is \(y+5=-3(x-1)\)
Part 2) The equation in slope intercept form is \(y=-3x-2\)
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
\(m=\frac{y2-y1}{x2-x1}\)
substitute the values
\(m=\frac{7+5}{-3-1}\)
\(m=\frac{12}{-4}\)
\(m=-3\)
Find the equation of the line into point slope form
\(y-y1=m(x-x1)\)
we have
\(m=-3\)
\(point\ (1,-5)\)
substitute
\(y+5=-3(x-1)\) ----> equation of the line in point slope form
Part 2) Rewrite the equation in slope-intercept form.
\(y=mx+b\)
we have
\(y+5=-3(x-1)\)
Convert to slope intercept form
Isolate the variable y
Distribute right side
\(y+5=-3x+3\)
Subtract 5 both sides
\(y=-3x+3-5\)
\(y=-3x-2\)
