Derive y=mx+b Worksheets Grade 8

1. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A line is drawn from the vertex at (0,0) to the midpoint of the hypotenuse. What is the equation of this line in slope-intercept form (y = mx + b)?
2. Matiu is tracking the growth of a young kauri tree in his backyard. When he first planted it, the tree was 45 centimeters tall. After 14 months, the tree had grown to 171 centimeters tall. Assuming the tree grows at a constant rate, write a linear equation in the form y = mx + b that represents the height of the tree (y) after x months.
3. Mason is training for a charity bike ride and tracks the distance he cycles each day. On day 0 (before training starts), he has already cycled 0 miles. After 12 days of training, he has cycled a total of 96 miles. Assuming he cycles at a constant rate each day, write a linear equation in the form y = mx + b that represents the total distance cycled (y) after x days.

…and 4 more problems

1. Find the equation of the line in y = mx + b form that passes through points (3, 11) and (7, 23).
2. Aisha is designing a wheelchair ramp for her school's new accessibility project. The ramp needs to rise 3 feet to reach the entrance. Building codes require that for every 1 foot of vertical rise, there must be at least 12 feet of horizontal run. If the ramp starts at ground level (0 feet) and follows a linear path, write the equation in the form y = mx + b that represents the height y of the ramp at any horizontal distance x from the starting point.
3. A quadrilateral is drawn on a coordinate plane with vertices at A(1, 2), B(5, 8), C(11, 8), and D(7, 2). A line is drawn connecting the midpoints of sides AB and CD. Find the equation of this line in slope-intercept form (y = mx + b).

…and 5 more problems

1. Liam is designing a rectangular garden. The length of the garden is 5 feet more than twice its width. If the perimeter of the garden is 82 feet, what is the equation in slope-intercept form (y = mx + b) that represents the relationship between the length (y) and the width (x) of the garden?
2. A line is drawn on a coordinate plane passing through points (2, 5) and (6, 13). Write the equation of this line in slope-intercept form (y = mx + b).
3. Olivia is helping her family track the water level in their rain barrel. When they started monitoring at noon (time 0 hours), the barrel already had 9 inches of water. After 7 hours, the water level had risen to 23 inches. Assuming the water level increases at a constant rate, write a linear equation in the form y = mx + b that represents the water level (y) in inches after x hours.

…and 4 more problems