Answer:
[tex]y-2 = -3(x-2)[/tex]
Step-by-step explanation:
Find the diagram to the question attached.
The standard equation of a line in point-slope form is expressed as:
[tex]y-y_0 = m(x-x_0)[/tex] where:
m is the slope of the line
[tex](x_0, y_0)[/tex] is coordinate point on the line
First is to get the slope of the line.
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
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)
[tex]m = \frac{8-2}{0-2}\\m = \frac{6}{-2}\\m = -3[/tex]
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)
[tex]y-y_0 = m(x-x_0)\\y-2 = -3(x-2)[/tex]
Hence the equation of the line in point-slope form is [tex]y-2 = -3(x-2)[/tex]
