Core Connections Algebra 2, 2013
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Core Connections Algebra 2, 2013 View details
1. Section 4.1
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Exercise 44 Page 181

Practice makes perfect
a Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept.

y= mx+ b The given equation is already in this form. Below we have highlighted the slope m and y-intercept b. y=-6/5x-7 ⇒ y= -6/5x+( -7) We can see that the slope is - 65 and the y-intercept is (0, -7).

b Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept.
y= mx+ bLet's rewrite our equation a little bit so that it more closely resembles this format. This will make it easier to identify the features of the equation.
3x-2y=10
3x=10+2y
3x-10=2y
3/2x-5=y
y=3/2x-5
The given equation is now in slope-intercept form. Below we have highlighted the slope m and y-intercept b. y=3/2x-5 ⇒ y= 3/2x+( -5) We can see that the slope is 32 and the y-intercept is (0, -5).
c 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. We will start by substituting the points into the Slope Formula.
m=y_2-y_1/x_2-x_1
m=4-( -2)/8- 5
â–Ľ
Simplify right-hand side
m=4+2/8-5
m=6/3
m=2
A slope of 2 means that for every 1 horizontal step in the positive direction, we take 2 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 2 x+b Now we will find 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 ( 5, -2).
y=2x+b
-2=2( 5)+b
â–Ľ
Solve for b
-2=10+b
-12=b
b=-12
A y-intercept of -12 means that the line crosses the y-axis at the point (0,-12).