Question

I don’t know how to solve this I need help please

Answer 1

Since the path of Grant is a line segment, the first step to solve the exercise is to find the slope of the line segment. For this, we can use the following formula:

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope of the line, and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through the line passes} \end{gathered}`

As we can see in the graph, the line segment passes through the points (8,0) and (-4,6). Then, we have:

`\begin{gathered} (x_1,y_1)=(8,0) \\ (x_2,y_2)=(-4,6) \\ m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(6-0)/(-4-8) \\ m=(6)/(-12) \\ \text{ Simplify} \\ m=(1\cdot6)/(-2\cdot6) \\ m=-(1)/(2) \end{gathered}`

Now that we have the slope of the line segment and a point which it passes, we can use the point-slope formula:

`y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula}`
`y-0=-(1)/(2)(x-8)`

Finally, we solve for y the above equation:

`\begin{gathered} y=-(1)/(2)(x-8) \\ \text{ Apply the distributive property} \\ y=-(1)/(2)\cdot x-(1)/(2)\cdot-8 \\ y=-(x)/(2)+(1)/(2)\cdot8 \\ y=-(x)/(2)+(8)/(2) \\ y=-(x)/(2)+4 \\ \text{ Reorder} \\ y=4-(x)/(2) \end{gathered}`

Therefore, the equation that represents the path of Grant is:

`$$\boldsymbol{y=4-(x)/(2)}$$`