SOLUTION: Find the slope and the y-intercept of the line 5x=7y+14 The slope is? The y-intercept is?

Question 266532: Find the slope and the y-intercept of the line
5x=7y+14
The slope is?
The y-intercept is?
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Put the eqn in slope-intercept form, y = mx + b
That means solve for y.
m is the slope
b is the y-intercept
I don't see any point in me doing it, but I'll check your answers if you email me via the thank you note.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
to find the slope, you put the equation into slope intercept form.

slope intercept form is found by solving for y.

the slope intercept form is y = mx + b where m is the slope and b is the y-intercept.

your equation is:

5x = 7y + 14

subtract 14 from both sides of the equation to get 7y = 5x - 14

divide both sides of the equation by 7 to get y = (5/7)x - (14/7)

your slope is (5/7) and your y-intercept is (14/7)

graph of your equation is shown below:

when x is 0, y is -2 (same as -(14/7).
that's your y-intercept.

for every 7 units to the right for x, y moves up 5 units.

when x is 0, y is -2.
when x is 7, y is 3.
that's a movement of up 5 for y when x moves right 7.
that's your slope (5/7) which is change in y divided by change in x.

your original equation is:

5x = 7y + 14

make x = 0 and you get 0 = 7y + 14
subtract 14 from both sides of equation to get 7y = -14
divide both sides by 7 to get y = -2 (y-intercept).
the y-intercept equals the value of y when x = 0.

to see if the slope is accurate, make x = 7 in the original equation.

5x = 7y + 14 becomes 5*7 = 7y + 14 becomes 35 = 7y + 14.
subtract 14 from both sides to get 7y = 35-14 which becomes 7y = 21.
divide both sides by 7 to get y = 3.

the original equation gives you the same results as the slope intercept form of the original equation which it should do so you're good all around.

your answer is:

slope = (5/7)

y-intercept = -2

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