Point-Slope to Slope-Intercept: 8th Grade Challenges

A line passes through the point (2, 3) with a slope of 4. Write the equation in point-slope form and convert it to slope-intercept form.

• y - 3 = 2(x - 2)

• y = 4x + 1

• y - 3 = 4(x - 2) and y = 4x - 5

• y - 3 = 3(x - 2)

A car rental company charges a flat fee of $50 plus $20 for each day rented. Write the equation in point-slope form using the point (1, 70) and convert it to slope-intercept form.

• C = 30d + 50

• C = 50d + 20

• C = 20d + 50

• C = 20d + 70

A gardener is planting a row of trees. If the first tree is planted at (0, 2) and the slope of the line representing the row is 3, write the equation in point-slope form and graph it.

• y - 2 = 2(x - 0)

• y + 2 = 3(x + 0)

• y - 2 = 2(x - 1)

• y - 2 = 3(x - 0)

A bike shop sells bikes for $200 each and charges a $50 assembly fee. Write the equation in point-slope form using the point (1, 250) and convert it to slope-intercept form.

• y = 150x + 100

• y = 200x + 50

• y = 200x - 50

• y = 250x + 50

A student scored 75 on their first test and improved by 5 points for each subsequent test. Write the equation in point-slope form and graph it starting from the point (1, 75).

• y - 80 = 5(x - 2)

• y - 75 = 10(x - 1)

• y - 75 = 5(x - 1)

• y = 5x + 70

A delivery service charges $10 for the first mile and $2 for each additional mile. Write the equation in point-slope form using the point (1, 12) and convert it to slope-intercept form.

• y = 10 + 2x

• y = 2x + 10

• y = 2x + 12

• y = 10x + 2

A restaurant's revenue can be modeled by the equation y - 500 = 50(x - 10), where x is the number of customers. Convert this to slope-intercept form and explain what the slope represents.

• y = 50x - 500, slope = -50

• y = 50x + 500, slope = 0

• y = 500x, slope = 500

• y = 50x, slope = 50

A train travels at a constant speed of 60 miles per hour. If it starts at a station 30 miles away from the city, write the equation in point-slope form and graph it.

• y - 30 = 60(x - 0)

• y - 30 = -60(x - 0)

• y - 30 = 30(x - 1)

• y + 30 = -60(x + 0)

A local gym charges a membership fee of $30 plus $10 per class. Write the equation in point-slope form using the point (3, 60) and convert it to slope-intercept form.

• y = 10x + 30

• y = 10x + 20

• y = 5x + 30

• y = 10x + 50

A photographer charges $100 for a session and $25 for each additional hour. Write the equation in point-slope form using the point (2, 150) and convert it to slope-intercept form.

• y = 100x - 50

• y = 25x + 50

• y = 50x + 25

• y = 25x + 100