find the equation of the line containing the given points (1,3) and (-3,-7). Express your answer in slope-intercept form.

## Equation of the line. Slope-intercept

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# 2 Answers

Hi Grace;

(1,3) and (-3,-7)

The slope is defined as the change-of-y divided by the change-of-x...

(y-y

_{1})/(x-x_{1})(3--7)/(1--3)

Subtracting a negative number is the same as adding a positive number...

(3+7)/(1+3)

10/4

2.5

Let's take one point and apply the point-slope formula. This will expand into the slope-intercept formula. I randomly select the first point...

(y-y

_{1})=m(x-x_{1})(y-3)=2.5(x-1)

y-3=2.5x-2.5

Let's add 3 to both sides...

3+y-3=2.5x-2.5+3

**y=2.5x+0.5**

This is slope-intercept format of...

y=mx+b, m is the slope and b is the y-intercept, the value of y when x=0.

Let's plug-in the other point to verify formula...

-7=[2.5(-3)]+0.5

-7=-7.5+0.5

-7=-7

Slope intercept form is the form y= mx+b

where m is the slope and b is the y-intercept.

First, find your slope and plug into the form above

slope can be remembered as "rise over run." and your "rise" will be Y2-Y2 or 3-(-7) = 10

the "run" will be X2- X1 or 1 - (-3) = 4

therefore the slope is (Y2 - Y1 ) / (X2 - X1) = 10/4 or 2.5

Now plug into the slope intercept form using either of your original points. I picked the point (1,3)

y = mx + b

3 = (2.5)(1) + b now you must solve for b

3 = 2.5 + b and b = 0.5

Therefore the equation of the line is y = 2.5x + 0.5

## Comments

_{1}or y_{2}. Your equation for slope is correct. It will produce the result of -10/-4 which is 10/4 which is 2.5. This is the same result we reached.Comment