Exercise 49 Page 191

Equations in point-slope form follow a specific format. y- y_1= m(x- x_1) In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. Here we are given that the line passes through known points.

x	1	2	3
y	- 3	1	5

To determine the slope of the line, we can calculate the slope by substituting only two points of the given table into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 1, - 3) & ( 2, 1)

m=1-( -3)/2- 1

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=1+3/2-1

AddSubTerms

Add and subtract terms

m=4/1

DivByOne

a/1=a

m=4

Now that we know the slope of the line is 4, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 2, 1). y-y_1=m(x-x_1) ⇕ y- 1= 4(x- 2) Since any point on the line could be used to form a point-slope equation, there are infinitely many possible equations. To write a unique equation for this line, we will rewrite it in slope-intercept form.

y-1=4(x-2)

Distr

Distribute 4

y-1=4x-4(2)

Multiply

Multiply

y-1=4x-8

AddEqn

LHS+1=RHS+1

y=4x-8+1

AddTerms

Add terms

y=4x-7

Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!