Answer:
The equation of line M in slope intercept form is [tex]y=\frac{3}{2}x+1[/tex]
The equation of line M in standard form is [tex]3x-2y=-2[/tex]
Step-by-step explanation:
step 1
Find the slope of line M
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(2,4) and (0,1)
substitute
[tex]m=\frac{1-4}{0-2}[/tex]
[tex]m=\frac{-3}{-2}[/tex]
[tex]m=\frac{3}{2}[/tex]
step 2
Find the equation of the line M in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{2}[/tex]
[tex]point\ (0,1)[/tex]
substitute
[tex]y-1=\frac{3}{2}(x-0)[/tex]
[tex]y-1=\frac{3}{2}x[/tex] ----> equation in point slope form
step 3
Find the equation of line M in slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y in the equation of the line in point slope form
[tex]y-1=\frac{3}{2}x[/tex]
Adds 1 both sides
[tex]y=\frac{3}{2}x+1[/tex]
step 4
Find the equation of the line M in standard form
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integers
we have
[tex]y=\frac{3}{2}x+1[/tex]
Multiply by 2 both sides
[tex]2y=3x+2[/tex]
[tex]3x-2y=-2[/tex] ---> equation in standard form
