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What is an equation of the line that passes through the point (8,-5) and is parallel to the line 5x + 4y = 24?
Question
What is an equation of the line that passes through the point (8,-5) and is parallel
to the line 5x + 4y = 24?
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Mathematics
5 years
2021-08-19T11:37:05+00:00
2021-08-19T11:37:05+00:00 1 Answers
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Answers ( )
Answer:
y=-5/4x+5
Step-by-step explanation:
Hi there!
We’re given the line 5x+4y=24 and we want to find the line parallel to it that passes through (8,-5)
Parallel lines have the same slopes
First, we need to find the slope of 5x+4y=24.
We’ll do that by converting 5x+4y=24 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b where m is the slope and b is the y intercept)
subtract 5x from both sides
4y=-5x+24
divide by 4 on both sides
y=-5/4x+6
since -5/4 is in the place where m should be, it is the slope.
So the equation of the line parallel to it will also have -5/4 as the slope
Here’s the equation so far in slope-intercept form:
y=-5/4x+b
we need to find b
because the equation will pass through (8,-5), we can use it to solve for b
substitute 8 as x and -5 as y
-5=-5/4(8)+b
multiply
-5=-10+b
add 10 to both sides
5=b
substitute 5 as b into the equation
y=-5/4x+5
That’s the equation of the line parallel to 5x+4y=24.
Hope this helps!