Question

Ted has already driven 100 miles to get to his ranch. Ted continues driving at a rate of 50 miles per hour. The relationship is graphed on the coordinate plane below. Write the equation that represents the relationship between x and y.

Answer 1

Answer:

y = (50mi/h)*x + 100mi

Step-by-step explanation:

Here we have a linear relationship.

Remember that a linear relationship can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Then the first thing we need to do is look at two points in the graph.

We can see that the line passes through the points (0, 100) and (2, 200)

Then the slope is:

a = (200 - 100)/(2 - 0) = 100/2 = 50

Then the equation is something like:

y = 50*x + b

To find the value of b we use the fact that the line passes through the point (0,100)

This means that when x = 0, y = 100.

then:

100 = 50*0 + b

100 = b

Then the equation that represents the relationship between x and y is:

y = 50*x + 100

If we also write the units, we get:

y = (50mi/h)*x + 100mi