Question

use the table to answer the question.
let x represent the time in minutes and let y represent the distance in feet. this table shows the relationship between time (in minutes) and distance (in feet).
relationship between time and
distance

time (minutes), x	1	2	3	4

use the table to create a formula for the given information.
(1 point)

Explanation:

Step1: Identify the relationship type

We check if the relationship between \(x\) (time) and \(y\) (distance) is linear. For a linear relationship, the slope \(m\) should be constant. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Taking the first two points \((1, 75)\) and \((2, 150)\): \(m=\frac{150 - 75}{2 - 1}=\frac{75}{1} = 75\).
Taking the next two points \((2, 150)\) and \((3, 225)\): \(m=\frac{225 - 150}{3 - 2}=\frac{75}{1}=75\).
Taking \((3, 225)\) and \((4, 300)\): \(m=\frac{300 - 225}{4 - 3}=\frac{75}{1}=75\). So it's a linear relationship.

Step2: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know \(m = 75\). To find \(b\), we can use one of the points. Let's use the point \((1,75)\).
Substitute \(x = 1\), \(y = 75\) and \(m=75\) into \(y=mx + b\):
\(75=75\times1 + b\)
\(75=75 + b\)
Subtract 75 from both sides: \(b=75 - 75=0\).

Step3: Write the formula

Since \(m = 75\) and \(b = 0\), the formula is \(y = 75x\).

Answer:

\(y = 75x\)