We want to see which linear equation represents the amount remaining on the gift card. We will see that the correct option is A:
y – 9.35 = −2.95(x – 7)
A linear equation in the point-slope form is written as:
y - y₁ = a*(x - x₁)
Where a is the slope of the line and (x₁, y₁) is a point on the line.
If we know two points on the line, (x₁, y₁) and (x₂, y₂) then we can write the slope as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use the two first points:
(2, 24.10)
(4, 18.20)
Then the slope is:
[tex]a = \frac{18.20 - 24.10}{4 - 2} = -2.95[/tex]
Then the equation is something like:
y - y₁ = -2.95*(x - x₁)
Now, from the given options the only one where (x₁, y₁) is a point on the line is the first option, where:
x₁ = 7
y₁ = 9.35
So the correct option is A:
y – 9.35 = −2.95*(x – 7)
If you want to learn more, you can read:
https://brainly.com/question/11897796
