Question

7. The point (-3,6) is on a line with a slope of 4.
a. Find two more points on the line.
b. Write an equation for the line.​

Answer 1

Equation: y=4x+18

y = 4x+b

(6) = 4(-3)+b

6 = -12 + b

6+12= -12 + 12 +b

18=b

1st Point: (1,22)

2nd Point: (2,26)

Answer 2

a. Two points that lie on a line are $(0,18),(1,22)$

b. An equation of a line is $y-6=4(x+3)$

An equation of a line that passes through point $\mathbf{(x_1,y_1)}$ such that it's slope is equal to $\mathbf{m}$ is given by $\mathbf{y-y_1=m(x-x_1)}$

Take $(x_1,y_1)=(-3,6)$

Take $m=4$

So, equation of a line is $\mathbf{y-6=4(x+3)}$

For $x=0$:

$y-6=12$

       $y=18$

So, point $\mathbf{(0,18)}$ lies on the line.

For $x=1$:

$y-6=16$

        $y=22$

So, point $\mathbf{(1,22)}$ lies on the line.

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