Question

Find an equation of the line passing through the pair of points. Write the equation in slope-intercept form. (2,8), and (8,2)

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Answer 1

`y=-x+10`

Explanation:

Hi there!

Slope intercept form:
`y=mx+b` where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Find the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where the two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (2,8),and (8,2)

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`m=(2-8)/(8-2)\\m=(-6)/(6)\\m=-1`

Therefore, the slope of the line is -1. Plug this into
`y=mx+b`:

`y=-x+b`

2) Find the y-intercept (b)

`y=-x+b`

Plug in a given point and solve for b

`8=-2+b`

Add 2 to both sides

`8+2=-2+b+2\\10=b`

Therefore, the y-intercept is 10. Plug this back into
`y=-x+b`:

`y=-x+10`

I hope this helps!