Question

12. Write an equation in slope-intercept form for a line that is (a) parallel (b) perpendicular to

the line y = -5x - 3 and has a y-intercept of 6.

Answer 1

a) Equation in slope-intercept form for a line that is parallel to the line y = -5x - 3 and has a y-intercept of 6 is y = -5x + 6

b) Equation in slope-intercept form for a line that is perpendicular to the line y = -5x - 3 and has a y-intercept of 6 is
`y = (1)/(5)x + 6`

Solution:

We have to find the equation in slope intercept form

The slope intercept form is given as:

y = mx + c

where "m" is the slope of line and "c" is the y -intercept

a) Equation in slope-intercept form for a line that is parallel to the line y = -5x - 3 and has a y-intercept of 6

Given line has equation y = -5x - 3

On comparing given equation y = -5x - 3 with slope intercept form, we get

slope of line "m" = -5

We know that slopes of parallel lines are equal

so slope of line parallel to given line is also -5

Now substitute m = -5 and c = 6 in slope intercept form

y = -5x + 6 is the required equation

b) Equation in slope-intercept form for a line that is perpendicular to the line y = -5x - 3 and has a y-intercept of 6

We already found that slope of line with equation y = -5x - 3 is -5

We know product of slopes of perpendicular lines are equal to -1

-5 x slope of line perpendicular to given line = -1

slope of line perpendicular to given line =
`(1)/(5)`

Now substitute m =
`(1)/(5)` and c = 6 in slope intercept form

`y = (1)/(5)x + 6`

Thus the required equation of line is found