Question

What is an equation of the line that passes through the points ( 0 , 4 ) and ( − 6 , 8 )

Answer 1

y=
`(-4)/(6)`x+4

Explanation:

The equation for a line can be written as y=mx+c, where m is the slope and c is the y-intercept (the value of y when x=0).

Given one of the points is (0,4), we know that when x=0, y is 4. This is our y-intercept.

The slope of a line with two points (
`x_(1)`,
`y_(1)`) and (
`x_(1)`,
`y_(1)`) can be found using the equation m=
`(y_(2)-y_(1) )/(x_(2) -x_(1) )`. Our two points are (0,4) and (-6,8), so let's use these to find the slope:

m=
`(y_(2)-y_(1) )/(x_(2) -x_(1) )`

m=
`(8-4)/(-6-0)`=
`(4)/(-6)`

Since we know the slope and y-intercept we can write the equation:

y=mx+c

y=
`(-4)/(6)`x+4