SOLUTION: what is the slope of a line parallel to the line whose equation is 10x-4y=24. what is my answer fully reduced

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Question 1173453: what is the slope of a line parallel to the line whose equation is 10x-4y=24. what is my answer fully reduced
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if the line is parallel, then the slope is the same and the y-intercept is different.

convert your equation to slope intercept form as follows:

start with 10x - 4y = 24
add 4y to both sides of the equation to get 10x = 4y + 24
subtract 24 from both sides of the equation to get 10x - 24 = 4y
switch sides to get 4y = 10x - 24
divide both sides by 4 to get y = 10/4 * x - 24/4
simplify to get y = 2.5x - 6

y = 2.5x - 6 is the slope intercept form of the equation of the standard form equation of 10x - 4y = 24.

the graph of the equation in both forms will show you the same line.
here's the graph.

any line with the same slope and a different y-intercept will be parallel to that line.

one example is y = 2.5x + 1 which is in slope intercept form.

the standard form of y = 2.5x + 1 is found as follows:
start with y = 2.5x + 1
subtract y from both sides of this equation and subtract 1 from both sides of this equation to get -1 = 2.5x - y
switch sides to get 2.5x - y = -1
multiply both sides of this equation by 2 to get 5x - 2y = -2

5x - 2y = -2 is the standard form equation of the slope intercept form equation of y = 2.5x + 1.

any multiple of the standard form of that equation will form the same line.

for example, 10x - 4y = -4 makes the same line on the graph as 5x - 2y = -2.

here's the graph of the equation of the line parallel to 10x - 4y = 24

the equations in red make the same red line.

the equations in blue make the same blue line.