Question

4) The line shown represents the amount of money

left on a gift card, y, after Mina buys lattes. After
buying 2 lattes, she has $2 left. What is an
equation of the line in point-slope form?

Answer 1

`y - 2 = -3(x - 2)`

Explanation:

The equation of the line in point-slope form is given by the formula,
`y - b = m(x - a)`, where,

(a, b) = coordinates of a point on the line.

`m = slope = (y_2 - y_1)/(x_2 - x_1)`

Given that after buying 2 lattes, she has $2 left, this represents a point on the line which is (a, b) = (2, 2). That is, when x = 2 lattes, y = $2.

Let's find the slope using the point (2, 2) and any other point on the line, say at x = 1, when y = 5, that's (1, 5).

`m = slope = (y_2 - y_1)/(x_2 - x_1) = (5 - 2)/(1 - 2)`

`= (3)/(-1)`

`m = slope = -3`

Plug m = -3, a = 2, and b = 2 into point-slope form.

`y - b = m(x - a)`

`y - 2 = -3(x - 2)`