Question

1. The table shows the relationship between y, the cost to rent a bicycle, and x, the amount of time the bicycle is

rented in hours.
Bicycle Rental Costs
Write a linear equation in slope-intercept form to represent the data shown in this table. Show your work.

Answer 1

The linear equation in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. Given the table, we can calculate the slope and y-intercept to write the equation.

Step-by-step explanation:

The linear equation in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the cost to rent a bicycle, y, is the dependent variable and the amount of time the bicycle is rented, x, is the independent variable.

Given the table, we can see that when x = 0, y = 7. When x = 1, y = 10.5. Using these two points, we can calculate the slope using the formula: m = (y2 - y1) / (x2 - x1). In this case, the slope is (10.5 - 7) / (1 - 0) = 3.5.

Next, we can substitute one of the points, let's say (0, 7), into the slope-intercept form equation and solve for b: y = mx + b. Substituting the values, we have 7 = 3.5(0) + b. Simplifying the equation, b = 7.

Therefore, the linear equation in slope-intercept form to represent the data shown in the table is y = 3.5x + 7.