Linear Equations and Graphing Concepts

This video tutorial covers linear equations in standard form, including converting from slope-intercept form, graphing lines, and solving word problems. It explains how to write equations in standard form, find slopes and intercepts, and graph lines using intercepts. The tutorial also includes a practical application through a word problem involving part-time jobs and earnings.

What is the standard form of a linear equation?

• AX + BY = C

• Y = MX + B

• Y = A(X - H)^2 + K

• AX^2 + BX + C = 0

In standard form, what must be true about the coefficients A, B, and C?

• They must be fractions.

• They must be negative.

• They must be integers.

• They must be positive.

How do you eliminate fractions when converting to standard form?

• Divide every term by the numerator.

• Add a constant to both sides.

• Multiply every term by the denominator.

• Subtract the fraction from both sides.

What is the first step in finding the equation of a line from a graph?

• Convert to point-slope form.

• Identify two points on the line.

• Find the midpoint of the line.

• Identify the x-intercept.

How can you determine the slope of a line from a graph?

• By finding the y-intercept.

• By calculating the area under the line.

• By counting the rise over run between two points.

• By measuring the angle with the x-axis.

What is the quickest way to graph a line in standard form?

• Convert to vertex form.

• Find the slope and y-intercept.

• Find the x and y-intercepts.

• Use the midpoint formula.

How do you find the x-intercept of a line?

• Find the midpoint of the line.

• Use the slope formula.

• Set x to zero and solve for y.

• Set y to zero and solve for x.

In the word problem, what does the variable X represent?

• The number of hours worked at $16 per hour.

• The number of hours worked at $10 per hour.

• The total money earned.

• The total number of hours worked.

If Manny works 10 hours at $16 per hour, how many hours must he work at $10 per hour to earn $300?

• 10 hours

• 20 hours

• 14 hours

• 16 hours

What is the y-intercept of the equation 10X + 16Y = 300?

• 18.75

• 10

• 30

• 16