Question

Henry records how many days he rides his bike and how far he rides each week. He rides the same distance each time . He rode 17 miles in 3 days, 24 miles in 4 days and 42 miles in 7 days Write and solve an equation to find how far he rides his bike in 10 days.

Answer 1

64 miles cuz he would take the shorter way

Answer 2

60 miles

Explanation:

a. Find the equation

Given:

• 3 days : 18 miles
• 4 days : 24 miles
• 7 days: 42 miles

Let y is the number of miles Henry can drive (dependent variable)

Let x is the number of days Henry can drive (independent variable)

The standard form of the equation is:

y = mx + b where m is the slope of the function

We know the slope is:

m =
`(y2 -y1)/(x2 -x1)` =
`(24 -18 )/(4-3)` = 6

=> y = 6x + b

To find b, we substitute 4 days : 24 miles into the above function:

24 = 6*4+ b

<=> b = 0

=> y = 6x

b. How far he rides his bike in 10 days.

Let x =10, we have y = 6*10 = 60 miles

Hope it will find you well.