Question

A map of the town that Hannah lives in can be represented by the Cartesian plane. Hannah starts off at $(-4, 9)$ and walks 10 units to the left and 7 units down to get to her new location. Along what line could she have walked to get to the new location directly from her old location? Express your answer in the form $ax+by=c$ where $c$ is a positive integer and $a$ and $b$ are integers not having any common factors other than 1.

Answer 1

To find the line that Hannah could have walked to get to her new location directly from her old location, we can use the concept of slope.

Step-by-step explanation:

To find the line that Hannah could have walked to get to her new location directly from her old location, we can use the concept of slope. The slope of a line is given by the formula: slope = (change in y)/(change in x). In this case, Hannah walked 10 units to the left and 7 units down, so the change in x is -10 and the change in y is -7. The equation of the line can be found using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the old location. Plugging in the values, we get: y - 9 = (-7/-10)(x - (-4)). Simplifying, we get: y - 9 = (7/10)(x + 4).