Exercise 15 Page 331

Let's start by plotting the x- and y-coordinates as points in a coordinate plane, then draw a line through them.

From the graph, we see that the data can be described with a linear equation. The easiest way to find it is to use slope-intercept form. Equations in this form follow a specific format. y= mx+b For an equation in this form, m is the slope and b is the y-intercept. Let's use two of the given points to calculate m and b. We will start by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 4,16) & ( 6,23)

m=23- 16/6- 4

SubTerms

Subtract terms

m=7/2

A slope of 72 means that for every 2 horizontal steps in the positive direction, we take 7 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 7/2 x+b To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 4, 16).

y=7/2x+b

SubstituteII

x= 4, y= 16

16=7/2( 4)+b

▼

Solve for b

Multiply

Multiply

16=14+b

SubEqn

LHS-14=RHS-14

2=b

RearrangeEqn

Rearrange equation

b=2

A y-intercept of 2 means that the line crosses the y-axis at the point (0,2). We can now complete the equation. y= 7/2x+2