Question

Find the equation for the line with the given properties. Sketch the graph of the line. Passes through (2, -5) and (7,3)

Answer 1

We have to find the equation of the line that passes through points (2,-5) and (7,3).

We can start by calculating the slope m as:

`m=(y_2-y_1)/(x_2-x_1)=(3-(-5))/(7-2)=(3+5)/(5)=(8)/(5)`

With one point and the slope, we can write the line equation in slope-point form and then rearrange it:

`\begin{gathered} y-y_2=m(x-x_2) \\ y-3=(8)/(5)(x-7) \\ y-3=(8)/(5)x-(56)/(5) \\ y=(8)/(5)x-(56)/(5)+3\cdot(5)/(5) \\ y=(8)/(5)x-(56)/(5)+(15)/(5) \\ 5y=8x-56+15 \\ 5y=8x-41 \\ -8x+5y+41=0 \\ 8x-5y-41=0 \end{gathered}`

The equation in general form is 8x-5y-41 = 0.

We can sketch it as: