So remember that <u>parallel lines have the same slope,</u> while <u>perpendicular lines have slopes that are negative reciprocals to each other.</u> But first, we have to find out the slope of the original equation. The easiest method to find the slope is to convert this standard form equation to slope-intercept form.
Firstly, subtract 6x on both sides of the equation:
Next, divide both sides by -4 and your slope-intercept form is
Now, looking at our slope-intercept form we see that the slope of the original equation is 3/2. Using what we know about parallel and perpendicular lines, <u>the slope of a parallel line is 3/2 and the slope of a perpendicular line is -2/3</u>
Answer:
f(x)=x-6
Step-by-step explanation:
Given : Parent function :
To Find : If you shift the linear parent function, f(x) = x, down 6 units, what is the equation of the new function?
Solution:
Parent function :
Shift the given function down by 6 units.
Rule : The graph f(x) shifts down by b units
So, f(x)→f(x)-b
So, Shift the given function down by 6 units.
So, f(x)→f(x)-6
f(x)=x
So, x→x-6
So, the new function is f(x)=x-6
Answer:
2 hours, 150 miles
Step-by-step explanation:
The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.
<h3>Separation distance</h3>Jason got a head start of 20 miles, so that is the initial separation between the two drivers.
<h3>Closure speed</h3>Jason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.
<h3>Closure time</h3>The relevant relation is ...
time = distance/speed
Then the time it takes to reduce the separation distance to zero is ...
closure time = separation distance / closure speed = 20 mi / (10 mi/h)
closure time = 2 h
Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.
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<em>Additional comment</em>
The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.
