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.

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

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 =

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

Thus the required equation of line is found

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