To find the slope from an equation, solve the equation for y.
The equation will have the form y = mx + b, called the slope-intercept form.
Then m = slope.
Let's solve your equation for y.
[tex] 2x + 7y = 21 [/tex]
Subtract 2x from both sides.
[tex] 7y = -2x + 21 [/tex]
Divide both sides by 7.
[tex] y = -\dfrac{2}{7} x + \dfrac{21}{7} [/tex]
[tex] y = -\dfrac{2}{7} x + 3 [/tex]
Now compare the equation above to y = mx + b.
m is the number that multiplies x, and it is the slope.
[tex] m = -\dfrac{2}{7} [/tex]
