In the standard (x, y) coordinate plane, what is the slope of the line with equation 7y - 3x = 21?

2 Answers
Nov 27, 2017

See a solution process below:

Explanation:

We can rewrite this equation in standard form. The standard form of a linear equation is: color(red)(A)x + color(blue)(B)y = color(green)(C)

Where, if at all possible, color(red)(A), color(blue)(B), and color(green)(C)are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

-3x + 7y = 21

color(red)(-1)(-3x + 7y) = color(red)(-1) xx 21

(color(red)(-1) xx -3x) + (color(red)(-1) xx 7y) = -21

3x + (-7y) = -21

color(red)(3)x + color(blue)(-7)y = color(green)(-21)

The slope of an equation in standard form is: m = -color(red)(A)/color(blue)(B)

Substituting gives:

m = (-color(red)(3))/color(blue)(-7) = 3/7

Nov 27, 2017

Slope = m = 3/7

Explanation:

7y-3x=21

This equation is in standard form ax+by=c

To find the slope of the equation, we want the equation in slope-intercept from y=mx+b where m is the slope

Begin by rearranging the equation to equal y

7ycolor(red)(-3x)=21

3x is being subtracted, so perform the opposite operation of addition to get 3x on the other side of the equation

7y=color(red)(3x)+21

Isolate y by dividing the opposite side of the equation by 7

color(blue)(7y)=3x+21

color(blue)((7y)/7)=(3x)/color(blue)(7)+21/color(blue)7

y=3/7x+3

Now the equation is in slope-intercept form

y=color(green)(3/7)x+3

y=color(green)mx+b

Remember, m is the slope

Slope = m = 3/7