y=-1.14x+7.57 (rounded). Now the equation is in a slope-intercept form and you can easily find the slope and y-intercept.

slope: -8/7 or -1.14

y-intercept: 7.57 or 7 4/7

The m=slope and b= y-intercept

8x + 7y =53

-8x -8x

7y= -8x + 53

/7 /7 /7

y= -8x + 53

/7 /7

slope is m= negative 8 over 7

and y-intercept is 53 over 7

-8x -8x

7y = -8x + 53

/7 /7

y = 1 1/7x + 9

y intercept = 9

slope aka gradient of a line 1 1/7

-8x -8x

7y = -8x + 53

/ 7 /7 /7

y = -8/7 x + 53/7

The equation for a line is:

y = mx+ b

where m = slope

therefore for your equation

m = -8/7