Question

What is an equation of the line that passes through the points ( −4 , − 6 ) and (4,4)?

Answer 1

`y = (5)/(4) x -1`

Explanation:

Find the slope of this line by using the slope formula:
`(y_2-y_1)/(x_2-x_1)`. Substitute both given points into this formula.

`((-6)-(4))/((-4)-(4)) \rightarrow(-10)/(-8) \rightarrow(-5)/(-4) =(5)/(4)`

The slope of the line is 5/4. Now this can be plugged into point-slope form since we have the point and the slope of the line.

Use any pair of given points, I'll be using (4,4).

Point-slope form:
`y-y_1=m(x-x_1)`

Substitute 4 for
`x_1`, 4 for
`y_1`, and 5/4 for m.

`y-(4)=(5)/(4) (x-(4))`

Simplify this equation.

`y-4=(5)/(4) (x-4)\rightarrow y-4=(5)/(4) x-5\rightarrow y = (5)/(4) x -1`

The equation in slope-intercept form of the line is
`y = (5)/(4) x -1`.

Answer 2

y=5/4x-1

Explanation:

-6-4/-4-4 = -10/-8 = 5/4 (slope)

y=5/4x+b

4=5/4(4)+b

b=-1

y=5/4x-1