Question

Erin walking to school and is traveling along the path that is represented by the equation y=4x-3. Joseph attends the same school as Erin and begins walking at the point (8,5) such that his path is parallel to Erin’s. What is the equation of the line that represents Joseph’s path?

Answer 1

To find the equation of Joseph's path parallel to Erin's path represented by y=4x-3, we can use the point-slope form of a linear equation. Joseph's path has the equation y=4x-27.

Step-by-step explanation:

To find the equation of Joseph's path, we need to know that parallel lines have the same slope. The equation of Erin's path is y = 4x - 3, where the slope is 4. So, to find the equation of Joseph's path, we can use the point-slope form of a linear equation. The slope will be the same as Erin's, which is 4, and we can use the point (8, 5) as Joseph's starting point.

Using the point-slope form, the equation of Joseph's path is y - 5 = 4(x - 8).

Simplifying the equation, we get y - 5 = 4x - 32.

Finally, rearranging the equation, we find the equation of Joseph's path is y = 4x - 27.