Mathematics: 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. .

Write the equation of the line that passes through

Ответ:

carlosd21151

12.03.2022

Mathematics

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

y=(-3/2)x-6

Step-by-step 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 $m=\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line}$ .

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

y=(-3/2)x-6