6x-5y+3=2x-2y-9

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

y=mx+b

Move all terms containing y to the left side of the equation.

Add 2y to both sides of the equation.

6x-5y+3+2y=2x-9

Add -5y and 2y.

6x-3y+3=2x-9

6x-3y+3=2x-9

Move all terms not containing y to the right side of the equation.

Subtract 6x from both sides of the equation.

-3y+3=2x-9-6x

Subtract 3 from both sides of the equation.

-3y=2x-9-6x-3

Subtract 6x from 2x.

-3y=-4x-9-3

Subtract 3 from -9.

-3y=-4x-12

-3y=-4x-12

Divide each term by -3 and simplify.

Divide each term in -3y=-4x-12 by -3.

-3y-3=-4x-3+-12-3

Cancel the common factor of -3.

Cancel the common factor.

-3y-3=-4x-3+-12-3

Divide y by 1.

y=-4x-3+-12-3

y=-4x-3+-12-3

Simplify each term.

Dividing two negative values results in a positive value.

y=(4)x3+-12-3

Divide -12 by -3.

y=4×3+4

y=4×3+4

y=4×3+4

Rewrite in slope-intercept form.

y=43x+4

y=43x+4

Using the slope-intercept form, the slope is 43.

m=43

Find the Slope 6x-5y+3=2x-2y-9