We have a direct variation. Distance, D, varies directly as time, t.
So D = Kt where K is the constant. In this case, speed. So D = Kt is our constant of variation.
If D = 150 miles and t = 4 hours
Then we have 150 = K (4)
K = 150/4 = 37.5. The constant of variation is 37.5.
If you keep traveling at a constant speed K = 37.5 and D = 200. We have
200 = 37.5 * t
t = 200/37.5 = 5.333 hours.
Answer:
No solution
Step-by-step explanation:
Step 1: Write out equations
y = -1/4x + 2
3y = -3/4x - 6
Step 2: Substitution
3(-1/4x + 2) = -3/4x - 6
Step 3: Distribute
-3/4x + 6 = -3/4x - 6
From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.
Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.
Answer:
A parallel y = 3x-1
B perpendicular y = -1/3x+9
Step-by-step explanation:
y = 3x-4 is written in slope intercept form (y=mx+b) so the slope is 3.
A. If the lines are parallel they have the same slope
m parallel is 3
Using point slope form
y-y1 = m(x-x1)
y-8 = 3(x-3)
Distribute
y-8 = 3x-9
Add 8 to each side
y-8+8 = 3x-9+8
y = 3x-1
This is slope intercept form
B If we want perpendicular lines, the slope is the negative reciprocal
m perpendicular is -(1/3) = -1/3
Using point slope form
y-y1 = m(x-x1)
y-8 = -1/3(x-3)
Distribute
y-8 = -1/3x+1
Add 8 to each side
y-8+8 = -1/3x+1+8
y = -1/3x+9
This is slope intercept form
