Question

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

Answer:

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

Step-by-step explanation:

Find the diagram to the question attached.

The standard equation of a line in point-slope form is expressed as:

$y-y_0 = m(x-x_0)$ where:

m is the slope of the line

$(x_0, y_0)$ is coordinate point on the line

First is to get the slope of the line.

$m = \frac{y_2-y_1}{x_2-x_1}$

If after buying 2 lattes, she has $2 left, hence one of the coordinate of the line is (2, 2). We can get the other coordinates from the graph. From the graph, it can be seen that when x = 0, y = 8. Hence the other coordinates is (0, 8)

$m = \frac{8-2}{0-2}\\m = \frac{6}{-2}\\m = -3$

Hence the slope is -3

Substitute m = -3 and the point (2, 2) into the formula to get the required equation (note that any of the points can be used)

$y-y_0 = m(x-x_0)\\y-2 = -3(x-2)$

Hence the equation of the line in point-slope form is $y-2 = -3(x-2)$