Linear Problem Solving

• 3

• -3

• 2

• -2

Answer explanation

To find the x-intercept, set y = 0 in the equation 2x - 3y = 6. This gives 2x = 6, so x = 3. Thus, the x-intercept is 3.

• (4, -1)

• (6, 0)

• (8, 1)

• (10, 2)

Answer explanation

To check which point lies on the line y = (1/2)x - 3, substitute the x-values of each point into the equation. For (4, -1): y = (1/2)(4) - 3 = -1. This is true, so (4, -1) is on the line. The other points do not satisfy the equation.

• 4

• 2

• 0

• -4

Answer explanation

To find the y-intercept, set x = 0 in the equation 4x + 2y = 8. This gives 2y = 8, so y = 4. Thus, the y-intercept is 4.

Determine the equation of the line that passes through the points (1, 2) and (3, 6).

Answer explanation

To find the equation of the line through (1, 2) and (3, 6), calculate the slope: (6-2)/(3-1) = 2. Using point-slope form with point (1, 2), we get y - 2 = 2(x - 1), simplifying to y = 2x. Thus, the correct answer is y = 2x.

If a line has a slope of 0, which of the following is true about the line?

• It is vertical.

• It is horizontal.

• It passes through the origin.

• It has no y-intercept.

Answer explanation

A line with a slope of 0 is horizontal, meaning it runs parallel to the x-axis. It does not rise or fall, which confirms that the correct answer is 'It is horizontal.'

Find the equation of the line with a slope of 5 and a y-intercept of -3.

Answer explanation

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Here, m = 5 and b = -3, so the equation is y = 5x - 3, which matches the first answer choice.

• 3

• -3

• 9

• -9

Answer explanation

To find the x-intercept, set y to 0 in the equation y = -3x + 9. This gives 0 = -3x + 9. Solving for x, we get 3. Thus, the x-intercept is 3.

Which of the following equations represents a line with an undefined slope?

Answer explanation

The equation x = 5 represents a vertical line, which has an undefined slope. In contrast, y = 5 and y = 0 represent horizontal lines with a slope of 0, while x = 0 is also a vertical line with an undefined slope.

A company charges a flat fee of $50 plus $20 per hour for their service. Write the linear function to represent the total cost in terms of the number of hours.

• C(x) = 20x - 50

• C(x) = 50x + 20

• C(x) = 50x - 20

• C(x) = 20x + 50

Samantha earns $15 per hour for tutoring and also receives a $20 bonus each week. Write the linear function to represent her total earnings in terms of the number of hours she works.

• E(x) = 20x - 15

• E(x) = 20x + 15

• E(x) = 15x + 20

• E(x) = 15x - 20