Question

The table below shows how much Lupe earns for each mile he walks for a library fundraiser.

| Miles Walked | Money Raised ($) |
| 0 | 50 |
| 1 | 60 |
| 2 | 70 |
| 3 | 80 |

Let R represent the number of dollars he raises for the fundraiser. Which equation represents how much Lupe will raise for m miles?

A. R = 50 + 10m
B. R = m + 50
C. R = 5 x 10m
D. R = 10 (m + 50)

Answer 1

A. R = m + 50 ..........

Answer 2

Option A is correct

R = 50 + 10m

Explanation:

Slope intercept form:

The equation of line is given by:

`y=mx+b` ....[1]

where,

m is the slope of the line and b is the y-intercept.

As per the statement:

The given table shows how much Lupe earns for each mile he walks for a library fundraiser.

Here, R represent the number of dollars he raises for the fundraiser and m represents the number of miles.

Formula for slope.

`\text{slope} = (y_2-y_1)/(x_2-x_1)`

from the given table.

Consider two points in the form of (m, R) i.e

(0, 50) and (1, 60)

then;

`\text{slope} = (60-50)/(1-0)`

⇒
`\text{slope} = (10)/(1)`

⇒Slope = 10

Using slope intercept form we have;

`R = 10m+b`

Substitute (2, 70) and solve for b.

70 = 10(2)+b

⇒70=20+b

Subtract 20 from both sides we have;

50 = b

or

b= 50

⇒R = 10m+50

Therefore, an equation represents how much Lupe will raise for m miles is, . R = 50 + 10m