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McGraw Hill Glencoe Algebra 1, 2012

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McGraw Hill Glencoe Algebra 1, 2012 View details

6. Graphing Inequalities in Two Variables

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Exercise 61 Page 322

Start by using the Slope Formula to find the slope.

y=8x-11

Practice makes perfect

An equation in slope-intercept form follows 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 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 ( 1,-3) & ( 2,5)

m=-3- 5/1- 2

▼

Simplify right-hand side

Subtract terms

m=-8/-1

- a/- b=a/b

m=8/1

a/1=a

m=8

A slope of 8 means that for every 1 horizontal step in the positive direction, we take 8 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 8 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 ( 2, 5).

y=8x+b

x= 2, y= 5

5=8 ( 2)+b

▼

Solve for b

Multiply

5=16+b

LHS-16=RHS-16

-11=b

Rearrange equation

b= - 11

A y-intercept of -11 means that the line crosses the y-axis at the point (0, -11). We can now complete the equation. y= 8x+( -11) ⇔ y=8x-11

Subchapter links

Check Your Understanding p.320

Practice and Problem Solving p.320-321

H.O.T. Problems p.321

Standardized Test Practice p.322

Spiral Review p.322

Skills Review p.322