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

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3