Question 266532
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:


{{{graph(600,600,-10,10,-10,10,(5/7)*x-(14/7))}}}


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