Question

1. solve the formula for m. y = mx + b

options:
a. m = y - (x + b)
b. m = (y - b)/x
c. m = y/x - b
d. m = y/b - x

1. solve the formula for y. -10x + 2y = 4

options:
a. y = 5x + 2 (circled)
b. y = 5x + 4
c. y = 2 + 10x
d. y = 28/x

1. solve the formula for c. ad + bc = 2

options:
a. c = 2/ad - b
b. c = 2/b - ad
c. c = b(2 - ad)
d. c = (2 - ad)/b (circled)

Explanation:

Question 3: Solve \( y = mx + b \) for \( m \)

Step 1: Subtract \( b \) from both sides

To isolate the term with \( m \), we subtract \( b \) from both sides of the equation \( y = mx + b \). This gives us \( y - b = mx \).

Step 2: Divide both sides by \( x \)

Now, to solve for \( m \), we divide both sides of the equation \( y - b = mx \) by \( x \) (assuming \( x
eq 0 \)). This results in \( m=\frac{y - b}{x} \).

Step 1: Add \( 10x \) to both sides

To isolate the term with \( y \), we add \( 10x \) to both sides of the equation \( - 10x+2y = 4 \). This gives \( 2y=10x + 4 \).

Step 2: Divide both sides by 2

Now, we divide each term on both sides of the equation \( 2y = 10x+4 \) by 2. So, \( y=\frac{10x + 4}{2}=5x + 2 \).

Step 1: Subtract \( ad \) from both sides

To isolate the term with \( c \), we subtract \( ad \) from both sides of the equation \( ad + bc=2 \). This gives \( bc=2 - ad \).

Step 2: Divide both sides by \( b \)

Now, we divide both sides of the equation \( bc = 2 - ad \) by \( b \) (assuming \( b
eq0 \)). This results in \( c=\frac{2 - ad}{b} \).

Answer:

\( m=\frac{y - b}{x} \) (corresponding to option b if the options are as per the image context)

Question 4: Solve \( -10x + 2y = 4 \) for \( y \)