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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

7. Writing Equations in Point-Slope Form

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Exercise 2 Page 183

First, use the given points to calculate the slope. Then, identify the y-intercept.

y=3/2x+2

Practice makes perfect

Equations written in slope-intercept form follow a specific format. y= mx+ b In this form, m is the slope and b is the y-intercept. We need to identify these values using the given graph.

Slope

Let's start by substituting the points given on the graph into the Slope Formula and calculating m.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -2,-1) & ( 2,5)

m=5-( -1)/2-( -2)

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Simplify right-hand side

a-(- b)=a+b

m=5+1/2+2

Add terms

m=6/4

a/b=.a /2./.b /2.

m=6/2/4/2

Calculate quotient

m=3/2

We calculated that the slope of the given equation is 32. Now, let's calculate the y-intercept and then write the equation in slope-intercepted form.

y-intercept

The y-intercept is the y-value where the line crosses the y-axis.

We can see that the function intercepts the y-axis at (0, 2). This means that the value of b is 2.

Writing the Equation

Now that we have the slope and the y-intercept, we can write our final equation. y= 3/2x+ 2

Subchapter links

Try It p.180-181

Self-Assessment for Concepts & Skills p.181

Self-Assessment for Problem Solving p.182

Review & Refresh p.183

Concepts, Skills, & Problem Solving p.183-184