Salazar is driving 70 miles per hour. At this rate, how long will it take for him to travel 840 miles?
1 answer:
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Answer:
Step-by-step explanation:
Vertically stretched. The action of vertically stretched is accomplished by altering a in
y = a* abs(x)
What that means is that you make a > 1. In this case, a = 2
So far, what you have is
y = 2*abs(x)
Six units down. The action of 6 units down is accomplished by a number added or subtracted to/from absolute(x). down is minus, up is plus.
y = 2*abs(x) - b. Since we are moving down, b<0
y = 2*abs(x) - 6
Four Units Right. This is the tough one because it is anti intuitive. You would think you should be adding something somewhere to get a right hand movement.
Not true.
To move right you subtract something in the brackets.
y = 2*abs(x - 4) - 6
Graph
Just to make things complete, I have graphed this for you. Desmos is wonderful for this kind of problem.
red: y = abs(x)
blue: y = 2*abs(x - 4) - 6
to find the point, find the location
realize that the shortest line that crosses through the origin and y=9x+8 is perpendicular to y=9x+8
perpendicular lines have slopes that multiply to get -1
y=9x+8 has a slope of 9
9*m=-1, m=-1/9
the slope of the mystery line is -1/9
since it passes through the origin, the y intercept is 0
y=(-1/9)x is the equation of the line from the point to the origin
find the intersection of this line and the original line
set them equal to each other
(-1/9)x=9x+8
multily both sides by 9
-x=81x+72
minus 81 both sides
-82x=72
divide both sides by -82
x=-36/41
find y
y=(-1/9)x
y=(-1/9)(-36/41)
y=4/41
the point is