Answer:
a. y = 2x - 4
b. y = -3x + 7
c. y = 5x - 3
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) is
[tex]y-y_1=m(x-x_1)[/tex]
So, for each part, we get:
Part a.
The slope m = 2 and it passes through the point (x1, y1) = (3, 2)
[tex]y-2=2(x-3)[/tex]
Then, we can solve the equation for y, so
[tex]\begin{gathered} y-2=2(x)-2(3) \\ y-2=2x-6 \\ y-2+2=2x-6+2 \\ y=2x-4 \end{gathered}[/tex]
Part b.
In the same way, replacing m = -3 and (x1, y1) = (1, 4), we get
[tex]\begin{gathered} y-4=-3(x-1) \\ y-4=-3x-3(-1) \\ y-4=-3x+3 \\ y-4+4=-3x+3+4 \\ y=-3x+7 \end{gathered}[/tex]
Part c.
Replacing m = 5 and (x1, y1) = (1, 2), we get:
[tex]\begin{gathered} y-2=5(x-1) \\ y-2=5(x)+5(-1) \\ y-2=5x-5 \\ y-2+2=5x-5+2 \\ y=5x-3 \end{gathered}[/tex]
So, the answers are:
a. y = 2x - 4
b. y = -3x + 7
c. y = 5x - 3
