Find the slope of the line described by each equation

7x-6y=42

quick way:

If the line is expressed in the form
Ax + By + C = 0
the slope is -A/B , note the value of C does not enter the picture.
so for 7x - 6y = 42
the slope is -7/(-6) = 7/6

or , by the usual grade 9 way
7x - 6y = 42
-6y = -7x + 42
y = -7x/-6 + 42/-6

y = (7/6)x - 7 ,,,, slope = 7/6

How does 7x become -7x

are you not familar with the basic fundamental rules of solving equations.

I "moved" the +7x from the left side of the equation to the right side of the equation
or

7x - 6y -7x = -7x + 42
-6y = -7x + 42
now divide every term by -6
etc

identify the slope and y-intercept of y - 16 = -4x . so is the slope is -4 and y-intercept is 16 correct ?

To find the slope of the line described by the equation 7x - 6y = 42, we can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope.

Step 1: Start with the given equation: 7x - 6y = 42.

Step 2: Rewrite the equation by isolating y:
7x - 42 = 6y.
Divide both sides by 6:
(7x - 42) / 6 = y.
Simplify:
(7/6)x - 7 = y.

Step 3: Compare the equation to the slope-intercept form (y = mx + b) and identify the slope.
The slope of the line is the coefficient of x, which is 7/6.

Therefore, the slope of the line described by the equation 7x - 6y = 42 is 7/6.