Question

Write an equation in slope-intercept form for the line that passes through (-10,0) and is parallel to y=3x-16

Answer 1

For two lines to be parallel, then their slopes are equal in value.

The equation given;

$y=3x-16$

Has its slope given as 3.

The slope of the line when given the equation is the coefficient of x.

Next step, we have a second line passing through the point (-10,0), and its slope is 3 (parallel to the first one given).

We have the following variables as;

$(x,y)=(-10,0),m=3$

The equation is slope-intercept form is;

$y=mx+b$

We can now substitute the values of, x, y and m and we would have;

$\begin{gathered} y=mx+b \\ 0=3(-10)+b \\ 0=-30+b \\ \text{Add 30 to both sides and we'll have;} \\ 0+30=30-30+b \\ 30=b \end{gathered}$

The value of b (the y-intercept) is 30.

The equation can now be properly written as;

$\begin{gathered} y=mx+b \\ y=3x+30 \end{gathered}$

ANSWER:

$y=3x+30$