Equation of the line. Slope-intercept

Question

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

Answer 1

Hi Grace;

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

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

(y-y₁)/(x-x₁)

(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-y₁)=m(x-x₁)

(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

 

 

 

Answer 2

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