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

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!