Question

Write the equation of the line that passes through the points (1,5) and (9,1). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

These are tough, you need a strategy and the formula to go with it, use the point slope formula { y-y1=m(x-x1) } where m = slope and (x1,y1 ) are the points from one of the given points.

find m .. then plug in your point to your formula ... as follows

Explanation:

given: (x1,y1)=(1,5) and (x2,y2)=(9,1)

m = y2-y2 / x2- x1

m = 1-5 / 9-1

m = -4 / 8

m = -1/2

use the give point (1,5) and plug in with the slope you just solved for

y-y1 = m (x-x1)

y-5 = -1/2 (x -1)

y-5 = -1/2x + 1/2

y = -1/2x +5 1/2

above is the slope intercept form y = mx +b :) see?

as a side note.. notice that either point (1,5) or (9,1) gets the same slope intercept equation? when it's plugged in, so just use which ever one seems easier to you.

Answer 2

This is the point-slope form.

`y - 5 = - (1)/(2) (x - 1)`

Explanation:

Let's find the slope first. Remember that:

`m = (y_2 - y_1)/(x_2 - x_1)`

Let's find the slope now.

`m = (1 - 5)/(9 - 1) = ( - 4)/( \: \: \: 8) = - (1)/(2)`

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Done. Remember that point-slope form is:

`y - y_1 = m(x - x_1)`

All we have to do now is plug in.

`y - 5 = - (1)/(2) (x - 1)`

And we are now done!