Question

Write the equation of the line that passes through the points (0, -6) and (-4, 0).

Show how you arrived at your answer.
What would be the EQUATION? I’m confused. Please help.

Answer 1

The slope is -3/2.

Explanation:

Hint: slope formula:

`\displaystyle (y_2-y_1)/(x_2-x_1)=(rise)/(run)`

`\displaystyle (0-(-6))/((-4)-0)=(6)/(-4)=(6/2)/(-4/2)=(3)/(-2)=-(3)/(2)`

`\Large \textnormal{Therefore, the slope is -3/2.}`

Answer 2

y=(-3/2)x+-6

or

y=(-3/2)x-6

Explanation:

We are going to use slope-intercept form to find the equation for this line.

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

y-intercept means where it crosses the y-axis; the x will be 0 here. Look the question gives us the y-intercept which is -6.

So we already know b which is -6.

y=mx+-6

Instead of finding the slope using the slope formula which you could.

I'm going to plug in the point (-4,0) into y=mx+-6 to find m.

So replace x with -4 and y with 0 giving you:

0=m(-4)+-6

0=-4m-6

Add 6 on both sides:

6=-4m

Divide both sides by -4:

6/-4=m

Reduce the fraction:

-3/2=m

The slope is -3/2.

Again you could use the slope formula which says
`m=(y_2-y_1)/(x_2-x_1) \text{ where } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line}`.

This is the same thing as lining the points up vertically and subtracting the points vertically then putting 2nd difference over first difference. Like this:

( 0 , -6)

-( -4 , 0)

---------------

4 -6

The slope is -6/4 which is what we got doing it the other way.

So the equation with m=-3/2 and b=-6 in y=mx+b form is

y=(-3/2)x+-6

or

y=(-3/2)x-6