Question

Find the equation of a straight line that passes through the points(-2,10) and (4,14)​

Answer 1

y =
`(2)/(3)`x + 11
`(1)/(3)`

Explanation:

The equation of a straight line is: y = mx+c where m is the slope of the line and c is the y-intercept of a line.

Slope =
`(rise)/(run)`

=
`(14-10)/(4-(-2))`

=
`(4)/(6)`

=
`(2)/(3)`

To find the y-intercept, we can use one of the points to apply for the equation before finding the y-intercept. I will be using the point (4,14).

y =
`(2)/(3)`x + c

14 =
`(2)/(3)`×4 + c

14 = 2
`(2)/(3)` + c

c = 14-2
`(2)/(3)`

c = 11
`(1)/(3)`

Thus, the y-intercept is 11
`(1)/(3)`.