Solving Linear Equations and Graphing

This video tutorial teaches how to graph lines not in slope-intercept form by converting equations into function notation. It covers solving two-step equations, graphing using slope-intercept form, simplifying fractions, and alternative methods to find slope and intercept without converting to function notation.

What is the first step in solving a two-step equation like 3 + 2y = 7?

• Divide both sides by 2

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 2

In the equation y = 3x - 4, what does the number 3 represent?

• The slope

• The constant term

• The y-intercept

• The x-intercept

When graphing a line, what is the significance of the y-intercept?

• It is where the line crosses the x-axis

• It is where the line crosses the y-axis

• It is the midpoint of the line

• It determines the slope of the line

What is a common mistake when simplifying fractions with two terms in the numerator?

• Subtracting the denominator from both terms

• Dividing only one term by the denominator

• Multiplying both terms by the denominator

• Adding the denominator to both terms

How do you convert the equation -4x + 2y = 12 to slope-intercept form?

• Add 4x to both sides and divide by 2

• Subtract 4x from both sides and multiply by 2

• Add 12 to both sides and divide by 4

• Subtract 12 from both sides and multiply by 4

What is the slope of the line represented by the equation 2y = 4x + 12?

• 3

• 2

• 4

• 1

In the equation 3x - 6y = -12, what is the y-intercept after converting to slope-intercept form?

• 4

• 3

• 2

• 1

How can you find the slope of an equation without converting it to slope-intercept form?

• By dividing the coefficient of x by the coefficient of y

• By dividing the coefficient of y by the constant

• By dividing the constant by the coefficient of x

• By dividing the opposite of the coefficient of x by the coefficient of y

What is the y-intercept of the equation 3x - 6y = -12 without converting it to slope-intercept form?

• -2

• 2

• -3

• 3

What is the final step in graphing a line once you have the slope and y-intercept?

• Calculate the midpoint

• Draw the line through the points

• Plot the x-intercept

• Find the x-intercept