3. A line goes through the points (3,4) and (-3,6). (a) What is the slope of the line? Show your work(b) Write the equation of the line in point-slope form. Show your work(c) Write the equation of the line in slope-intercept form. Show your work.

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 formPart 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 ydistribute 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