Graphing Linear Equations & Finding Intercepts (Grade 8)

A park is being designed with two main entrances. The first entrance is at the point (2, 3) and the second entrance is at (6, 7). Write the equation of the line that connects these two points. What are the x and y intercepts of this line?

• Line equation: y = 2x - 1; x-intercept: 0; y-intercept: 2.

• Line equation: y = x + 1; x-intercept: -1; y-intercept: 1.

• Line equation: y = -x + 5; x-intercept: 5; y-intercept: 5.

• Line equation: y = 3x - 6; x-intercept: 2; y-intercept: 6.

A car rental company charges a flat fee of $50 plus $20 for each day the car is rented. If the total cost for renting a car for 3 days is $110, find the equation that represents the total cost based on the number of days rented. Identify the x and y intercepts.

• C = 50 + 25x; x-intercept: (-1.5, 0), y-intercept: (0, 50)

• C = 50 + 15x; x-intercept: (-3.33, 0), y-intercept: (0, 50)

• C = 50 + 20x; x-intercept: (-2, 0), y-intercept: (0, 60)

• C = 50 + 20x; x-intercept: (-2.5, 0), y-intercept: (0, 50)

A school is planning to build a new sports field. The coordinates of the two corners of the field are (1, 2) and (5, 6). Determine the equation of the line that represents the boundary of the field. What are the x and y intercepts?

• Equation: y = 0.5x + 2; x-intercept: -4; y-intercept: 2

• Equation: y = -x + 3; x-intercept: 3; y-intercept: 3

• Equation: y = 2x - 1; x-intercept: 2; y-intercept: 2

• Equation: y = x + 1; x-intercept: -1; y-intercept: 1

A delivery service charges $15 for the first mile and $5 for each additional mile. If the total cost for a delivery of 4 miles is $35, write the equation that models the cost based on the distance. Identify the x and y intercepts.

• The equation is C(x) = 10 + 5(x - 1). The y-intercept is (0, 15) and the x-intercept is (-3, 0).

• The equation is C(x) = 15 + 5(x - 1). The y-intercept is (0, 10) and the x-intercept is (-2, 0).

• The equation is C(x) = 20 + 5(x - 2). The y-intercept is (0, 5) and the x-intercept is (-1, 0).

• The equation is C(x) = 15 + 10(x - 1). The y-intercept is (0, 15) and the x-intercept is (-1.5, 0).

Two friends are walking in a straight line from point A (0, 0) to point B (4, 8). Write the equation of the line that represents their path. What are the x and y intercepts?

• Equation: y = 0.5x; x-intercept: (4, 0); y-intercept: (0, 8)

• Equation: y = 4x; x-intercept: (0, 4); y-intercept: (2, 0)

• Equation: y = 2x; x-intercept: (0, 0); y-intercept: (0, 0)

• Equation: y = x; x-intercept: (2, 0); y-intercept: (0, 2)

A farmer has two fields. The first field is at the point (3, 4) and the second field is at (7, 10). Write the equation of the line that connects these two fields. Identify the x and y intercepts of this line.

• y = 3x - 5; x-intercept: 5/3; y-intercept: -5

• y = 0.5x + 2; x-intercept: -4; y-intercept: 2

• y = 2x + 1; x-intercept: -1; y-intercept: 1

• y = 1.5x + 0.5; x-intercept: -1/3; y-intercept: 0.5

A bike rental shop charges a one-time fee of $10 plus $5 for each hour the bike is rented. If a customer pays $35, how many hours did they rent the bike? Write the equation and identify the x and y intercepts.

• 5 hours

• 10 hours

• 7 hours

• 3 hours

A city is planning to build a new road that connects two points: (2, 5) and (8, 11). Write the equation of the road. What are the x and y intercepts?

• Equation: y = 3x - 1; x-intercept: 1/3; y-intercept: -1

• Equation: y = x + 3; x-intercept: -3; y-intercept: 3

• Equation: y = -x + 7; x-intercept: 7; y-intercept: 7

• Equation: y = 2x + 1; x-intercept: -1; y-intercept: 1

A local bakery sells cupcakes for $2 each and cookies for $1 each. If a customer buys 10 items for a total of $18, write the equation that represents the relationship between the number of cupcakes (x) and cookies (y). Identify the x and y intercepts.

• The equation is 2x + y = 18. x-intercept: (9, 0), y-intercept: (0, 18).

• 2x + 3y = 18

• x-intercept: (10, 0), y-intercept: (0, 10)

• 2x + y = 20

A train travels from station A at (1, 2) to station B at (5, 6). Write the equation of the line that represents the train's path. What are the x and y intercepts?

• Equation: y = -x + 8; x-intercept: 8; y-intercept: 8

• Equation: y = 2x - 2; x-intercept: 2; y-intercept: 2

• Equation: y = x + 1; x-intercept: -1; y-intercept: 1

• Equation: y = 3x - 4; x-intercept: 4/3; y-intercept: -4