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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

3. Slope-Intercept Form

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Exercise 27 Page 312

Identify the y-intercept. Then, find another point that lies on the grid.

y=5/2x-1/2

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 graph.

y-intercept

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

y-intercept

We can see that the function intercepts the y-axis at ( 0, - 12). This means that the value of b is - 12. y= mx+( -1/2)

Slope

To find the slope, we will trace along the line on the given graph until we find a lattice point, which is a point that lies perfectly on the grid lines.

Finding a Lattice Point

Here we have identified (1,2) as our second point. We will now substitute the points into the Slope Formula and calculate the slope.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,- 1/2) & ( 1,2)

m=2 - ( - 1/2)/1- 0

a-(- b)=a+b

m=2+1/2/1-0

Write as a fraction

m=2/1+1/2/1-0

a/b=a * 2/b * 2

m=4/2+1/2/1-0

Add fractions

m=5/2/1-0

Subtract term

m=5/2

The value of the slope m is 52.

Writing the Equation

Now that we have the slope and the y-intercept, we can write our final equation. y= 5/2x+( -1/2) ⇔ y=5/2x-1/2

Subchapter links

Lesson Check p.311

Practice and Problem-Solving Exercises p.312-314

Standardized Test Prep p.314

Mixed Review p.314