Exercise 2 Page 175

The formula for slope can be written as: m=y_2-y_1/x_2-x_1, where m is the slope and (x_1,y_1) and (x_2,y_2) are two arbitrary points on the line. We have been given a slope of 4 and a point on the line, ( 3, -2). If we substitute this information into the Slope Formula, we have: 4=y_2-( -2)/x_2- 3. We can simplify this equation to be in the point-slope form, y-y_1=m(x-x_1). First, we can remove the subscripts because there is only one of each variable.

4=y_2-(-2)/x_2-3

Rewrite

Rewrite y_2 as y

4=y-(-2)/x_2-3

Rewrite

Rewrite x_2 as x

4=y-(-2)/x-3

Next we can simplify and use inverse operations to rearrange the equation to be in the correct form.

4=y-(-2)/x-3

SubNeg

a-(- b)=a+b

4=y+2/x-3

MultEqn

LHS * (x-3)=RHS* (x-3)

4(x-3)=y+2

RearrangeEqn

Rearrange equation

y+2=4(x-3)

As we have shown, the Slope Formula and the point-slope form are very closely related. We can easily find one when given the other.