Answer:
Part a) The slope is [tex]m=-\frac{1}{3}[/tex]
Part b) The equation in point slope form is [tex]y-4=-\frac{1}{3}(x-3)[/tex]
Part c) The equation in slope-intercept form is [tex]y=-\frac{1}{3}x+5[/tex]
Step-by-step explanation:
we have the points (3,4) and (-3,6)
Part a) What is the slope of the line?
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the given points
[tex]m=\frac{6-4}{-3-3}[/tex]
[tex]m=\frac{2}{-6}[/tex]
[tex]m=-\frac{1}{3}[/tex]
Part b) Write the equation of the line in point-slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]point\ (3,4)[/tex]
substitute
[tex]y-4=-\frac{1}{3}(x-3)[/tex] ---> equation in point slope form
Part c) Write the equation of the line in slope-intercept form
[tex]y=mx+b[/tex]
we have
[tex]y-4=-\frac{1}{3}(x-3)[/tex]
Isolate the variable y
distribute right side
[tex]y-4=-\frac{1}{3}x+1[/tex]
Adds 4 both sides
[tex]y=-\frac{1}{3}x+1+4[/tex]
[tex]y=-\frac{1}{3}x+5[/tex] ---> equation in slope intercept form
