Question

Find an equation for the line which passes through (-1,3) and is perpendicular to the line containing (0,3) and (4,7). The equation of the line is . (Simplify your answer. Type your answer in slope-intercept form.)

Answer 1

Equation of the line is y = -x + 4

Explanation:

When the two lines having their slopes
`m_(1)` and
`m_(2)` are perpendicular to each other then
`m_(1)* m_(2)=-1`

If
`m_(1)` is the slope of the line passing through two points (0, 3) and (4, 7) then

`m_(1)=(y-y')/(x-x')`

=
`(7-3)/(4-0)`

= 1

Now slope of the second line perpendicular to first line will be

`m_(2)` =
`-(1)/(m_(2) )`

`m_(2)` = -1

Slope intercept form of the equation of a line is represented by

y = mx + c

where m = slope

c = y intercept

Since the line is passing through (-1, 3) and slope = -1, therefore,

3 = -1 + c

c = 4

Now we plug in these values in the equation.

y = -x + 4

Equation of the line is y = -x + 4