Find an equation of the line that passes through the given points.

The equation of a line is given by the formula **y=
mx+b.**

This is known as the **slope-intercept form** of a linear equation. It is called a linear equation because when you graph this equation all of the points make a straight line.

In this equation **m = slope**. The slope = rise over run or "change in y over change in x.

To find the slope you would use the formula **m=y2-y1/x2-x1**

We will label our points:** X1**=-13,** X2**=20, **
Y1**= 13,** Y2**=-53

We will insert the points into our formula , m= (-53)- 13/20-(-13) = -66/33= **
-2**

**Therefore our slope is m= -2**

Next we need to find **b** which is the**
y-intercept. This is the value of y when x = 0**

To find the** y intercept**, we can use 2 methods:

• Method 1:

Since we know the points and the slope, we can plug one pair of them (it doesn't matter which pair) into our equation
**y-mx +b,** We will use the points (-13,13)

13 =-2(-13) +b)

13= 26+b

We will subtract 26 both sides to isolate b.

13-26= 26-26+b

**-13 =b (Therefore b or the "y-intercept=-13)**

• Method 2

Since we know the points and the slope, we can use the point-slope formula to find the y -intercept.

The point-slope formula is y-y1= m(x-x1) We will use the points (13,-13, the points we have identified as (x1,y1), Again we could have used either pair.

Y-13= -2(x-(-13) )

y-13= -2x-26

We will add 13 to both sides to isolate Y

Y-13+13= -2x-26+13

Y= -2x-13** (Therefore b or the "y-intercept=-13)**

Therefore the equation of the line is: **Y= -2X-13**

To verify our solution we will substitute both set of points into the equation.

(-13,13)

• 13 = -2(-13)-13

• 13= 26-13

• **13=13**

(20,-53)

- -53 = -2(20)-13
- -53 = -40 - 13
**-53= -53**

**We have verified our equation of the** **line**,** y=
-2x-13**

**M (Slope) = -2
**

**B (Y-Intercept) =
-13**