Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
5. Standard Form
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Exercise 70 Page 328

Start by finding the slope.

Point-Slope Form: y-2= 43(x-3)
Slope-intercept form: y= 43x -2

Practice makes perfect
In order to write both the slope-intercept form and the point-slope form, we need the slope of the line. To find the slope, we will use the given points and the Slope Formula.
m=y_2-y_1/x_2-x_1
m=2-( -2)/3- 0
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Simplify
m=2+2/3-0
m=4/3
Now that we know the slope, let's form our equations. We will find them one at a time.

Point-Slope Form

Equations in point-slope form follow a specific format.

y- y_1= m(x- x_1) In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. Since we know the slope of the line is 43, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 3, 2). y- 2= 4/3(x- 3) Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!

Slope-Intercept Form

Equations in slope-intercept form also follow a specific format. y= mx+b, In this form, m represents the slope of the line and b represents the y-intercept. We already calculated the slope as m= 43 above. The next step is to substitute one of the points into the equation and solve for the y-intercept, b. Let's use the point ( 0, -2).
y=4/3x+b
-2=4/3* 0+b
-2=b
b=-2
Now that we know the y-intercept lies at (0,-2), we have what we need to write a slope-intercept form equation. y= 4/3x+(-2) ⇔ y=4/3x-2