Answer:
[tex] y - 2 = -3(x - 2) [/tex]
Step-by-step explanation:
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]
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).
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 2}{1 - 2} [/tex]
[tex] = \frac{3}{-1} [/tex]
[tex] m = slope = -3 [/tex]
Plug m = -3, a = 2, and b = 2 into point-slope form.
[tex] y - b = m(x - a) [/tex]
[tex] y - 2 = -3(x - 2) [/tex]
