Question

What is the equation of the line that passes through (11,8) and (6,-12)

Answer 1

y = 4x - 36

Step-by-step explanation

We want to find the equation of the line that passes through the two given points.

To do that, we will use the point-slope formula:

y - y1 = m(x - x1)

where m = slope

To find the slope, we have to use the formula for slope:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

We have that:

(x1, y1) = (6, -12)

(x2, y2) = (11, 8)

Therefore:

`\begin{gathered} m\text{ = }\frac{8\text{ - (-12)}}{11\text{ - 6}}\text{ = }\frac{8\text{ + 12}}{11\text{ - 6}} \\ m\text{ = }(20)/(5) \\ m\text{ = 4} \end{gathered}`

Now, we use the formula:

y - (-12) = 4(x - 6)

y + 12 = 4x - 24

y = 4x - 24 - 12

y = 4x - 36

That is the equation of the line.