Question

Find the slope and the y-intercept of the line: 6x + 7y = 52

Answer 1

Slope is -6/7

Y-intercept is 52/7

Explanation:

6x + 7y = 52

6x - 6x + 7y = 52 -6x

1/7 (7y = -6x + 52) 1/7

y = -6/7x + 52/7

Answer 2

`slope = - (6)/(7) \\ y-intercept = 7 (3)/(7)`

Explanation:

Let's rewrite the equation into the form of y=mx+c, where m is the slope and c is the y-intercept.

6x +7y= 52

7y= -6x +52 (-6x on both sides)

`y = - (6)/(7) x + 7 ( 3)/(7)`

Thus,

`slope = - (6)/(7)`

`y-intercept = 7 (3)/(7)`

Alternatively, since y-intercept is when the line cuts through the y- axis (at x=0), substitute x= 0 to find the y-intercept.

6x +7y= 52

When x=0,

6(0) +7y= 52

7y= 52

y= 52 ÷7 (÷7 on both sides)

`y = 7 (3)/(7)`