Transforming Linear Equations: From Standard to Slope-Intercept Form

The video tutorial covers solving equations for y in slope-intercept form. It begins with an introduction to the concept and proceeds with five examples, each demonstrating different techniques and considerations when rearranging equations. The tutorial emphasizes understanding the roles of m and b in the equation y = mx + b and provides step-by-step guidance for each example. The video also highlights common mistakes and offers tips for correctly solving equations.

What is the goal when solving for y in an equation?

• To get the equation in the form y = mx + b

• To isolate x on one side

• To find the value of x

• To eliminate all variables

In the equation 2x - 3y = 24, what is the first step to solve for y?

• Multiply both sides by 3

• Divide both sides by 2

• Subtract 2x from both sides

• Add 3y to both sides

After moving the x term in the equation 2x - 3y = 24, what is the next step?

• Subtract 24 from both sides

• Multiply both sides by -3

• Divide both sides by -3

• Add 24 to both sides

In the equation x + y = 0, what is the value of the slope (m)?

• Undefined

• 0

• -1

• 1

What is the y-intercept (b) in the equation x + y = 0?

• 1

• 0

• -1

• Undefined

In the equation -4x + 5y = 40, what is the first step to solve for y?

• Multiply both sides by 4

• Divide both sides by 5

• Subtract 5y from both sides

• Add 4x to both sides

After moving the x term in the equation -4x + 5y = 40, what is the next step?

• Divide both sides by 5

• Multiply both sides by 5

• Subtract 40 from both sides

• Add 40 to both sides

In the equation 2y = 8x - 4, what is the final step to solve for y?

• Divide both sides by 2

• Subtract 8x from both sides

• Multiply both sides by 2

• Add 4 to both sides

What happens to the negative sign when dividing a negative number by another negative number?

• It becomes positive

• It remains negative

• It is eliminated

• It becomes zero

In the equation 2y = 8x - 4, what is the slope (m) after solving for y?

• 8

• 4x

• 2

• 4