Answer:
[tex] y - 2 = -3(x - 2) [/tex]
Step-by-step explanation:
Given that after she buys 2 lattes, she has $2 left, this represents a point on the line in the graph, which is (2, 2).
Point-slope form of equation for a line is given as [tex] y - b = m(x - a) [/tex]. Where,
(a, b) = a point on the line
m = slope
The equation of the line in point-slope form is given by the formula, [tex] y - b = m(x - a) [/tex], where,
(a, b) = coordinates of a point on the line.
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
We already have values for (a, b) = (2, 2), let's find the slope (m).
Using (2, 2) and any point on the line, such as (0, 8), we can find the slope as follows:
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 2}{0 - 2} [/tex]
[tex] = \frac{6}{-2} [/tex]
[tex] m = -3 [/tex]
Now we know that a = 2, b = 2 , and m = -3. Let's plug in this values into the point-slope equation as shown below:
[tex] y - b = m(x - a) [/tex]
[tex] y - 2 = -3(x - 2) [/tex]
