Question

I really need help on this question!!!

Answer 1

Answer:

The x-intercept is (6,0).

The y-intercept is (0,-21/2).

Step-by-step explanation:

So we are told this is a line.

Linear equations in the form y=mx+b tell us the slope,m, and the y-intercept,b.

So we are going to write our equation in this form to determine x- and y- intercept.

Let's begin.

First thing I'm going to is compute the slope.  The slope can be found by lining up the points vertically and subtracting them vertically then put 2nd difference over 1st difference.

Let's do that:

 (   -10  ,  -28)

- (    -6  ,   -21)

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

   -4             -7

So the slope is -7/-4 which is 7/4.

Now we know our equation to be in this form

y=(7/4)x+b

Use one of the points along with y=(7/4)x+b to find b.

Doesn't matter which one, you get to choose.

How about (-2,-14)?

-14=(7/4)(-2)+b

-14=-7/2+b

Add 7/2 on both sides:

-14+7/2=b

-21/2=b

So our equation is

$y=\frac{7}{4}x-\frac{21}{2}$

So we already know the y-intercept is (0,-21/2).

We knew this because we were putting into slope-intercept form.

Now to find the x-intercept, set y=0 and solve for x:

$0=\frac{7}{4}x-\frac{21}{2}$

Clear the fractions; multiply both sides by 4:

$0=7x-42$

Add 42 on both sides:

$42=7x$

Divide both sides by 7:

$\frac{42}{7}=x$

So x=6

The x-intercept is (6,0).