Question

Please help this is due in 30 mins!!

Write the equation of the line that passes through the points (4,7) and (-7,-5). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

Answer:
`y - 7 = (12)/(11)(x - 4)\\\\`

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Step-by-step explanation:

Let's first find the slope of the line through these given points.

`(x_1,y_1) = (4,7) \text{ and } (x_2,y_2) = (-7,-5)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (-5 - 7)/(-7 - 4)\\\\m = (-12)/(-11)\\\\m = (12)/(11)\\\\`

Then we'll apply point-slope to finish up the problem.

`y - y_1 = m(x - x_1)\\\\y - 7 = (12)/(11)(x - 4)\\\\`

Normally we would distribute the 12/11 value through and then isolate y; however, your teacher specifically mentioned to write the answer in point-slope form.

There's nothing really special about the selection of (x1,y1) as (4,7) since we could have easily swapped the given points and used (x1,y1) = (-7,-5) instead. The order of the points does not matter.

In other words, an alternative answer would be

`y - y_1 = m(x - x_1)\\\\y - (-5) = (12)/(11)(x - (-7))\\\\y + 5 = (12)/(11)(x +7)\\\\`

I'll stick with the first equation since (4,7) was listed first.