Question

standard form to slope - intercept form worksheet practice directions: convert the following equations into slope - intercept form. make sure to bubble in your answers below on each page so that you can check your work. show all of your work! 1. $x - 2y = - 20$ 2. $2x + 6y = - 18$ 3. $21x - 3y = 36$ 4. $32x + 8y = 96$ 5. $60x - 5y = 115$ 6. $15x - 75y = - 135$ 7. $72x + 12y = 156$ answers bubble in your answers below for problems #1 - 7. $y = - \frac{1}{2}x + 10$ $y = \frac{1}{5}x - 9$ $y = - 6x + 13$ $y = 7x - 12$ $y = \frac{1}{3}x + 3$ $y = \frac{1}{5}x + 9$ $y = 12x - 23$ $y = - 7x + 12$ $y = - \frac{1}{3}x - 3$ $y = \frac{1}{3}x + 3$ $y = - \frac{1}{5}x + 9$ $y = - \frac{1}{3}x - 3$ $y = 6x + 13$ $y = - 4x + 12$

Explanation:

Let's solve problem 1: \( x - 2y = -20 \) (converting to slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept)

Step 1: Isolate the \( y \) term

We start with the equation \( x-2y=-20 \). Subtract \( x \) from both sides of the equation.
\( x - 2y-x=-20 - x \)
Simplifying the left - hand side, \( x - x-2y=-20 - x \), so \( - 2y=-x - 20 \)

Step 2: Solve for \( y \)

Divide every term in the equation \( -2y=-x - 20 \) by \( - 2 \) to get \( y \) by itself.
\( y=\frac{-x}{-2}+\frac{-20}{-2} \)
Simplify the fractions: \( y = \frac{1}{2}x + 10 \)

Let's solve problem 2: \( 2x + 6y=-18 \)

Step 1: Isolate the \( y \) term

Start with \( 2x + 6y=-18 \). Subtract \( 2x \) from both sides.
\( 2x+6y - 2x=-18 - 2x \)
Simplifying the left - hand side, \( 6y=-2x - 18 \)

Step 2: Solve for \( y \)

Divide every term in \( 6y=-2x - 18 \) by \( 6 \)
\( y=\frac{-2x}{6}+\frac{-18}{6} \)
Simplify the fractions: \( y=-\frac{1}{3}x - 3 \)

Let's solve problem 3: \( 21x-3y = 36 \)

Step 1: Isolate the \( y \) term

Start with \( 21x-3y = 36 \). Subtract \( 21x \) from both sides.
\( 21x-3y-21x=36 - 21x \)
Simplifying the left - hand side, \( -3y=-21x + 36 \)

Step 2: Solve for \( y \)

Divide every term in \( -3y=-21x + 36 \) by \( - 3 \)
\( y=\frac{-21x}{-3}+\frac{36}{-3} \)
Simplify the fractions: \( y = 7x-12 \)

Let's solve problem 4: \( 32x + 8y=96 \)

Answer:

s:

1. \( y=\frac{1}{2}x + 10 \)
2. \( y = -\frac{1}{3}x-3 \)
3. \( y = 7x-12 \)
4. \( y=-4x + 12 \)
5. \( y = 12x-23 \)
6. \( y=\frac{1}{5}x+\frac{9}{5} \) (or \( y = 0.2x+1.8 \))
7. \( y=-6x + 13 \)