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

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

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Answer 1 · 2017-11-27T15:27:53

See a solution process below:

Explanation:

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

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

$- 3 x + 7 y = 21$ $-3x + 7y = 21$

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

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

$3 x + (- 7 y) = - 21$ $3x + (-7y) = -21$

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

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

Substituting gives:

$m = \frac{- 3}{- 7} = \frac{3}{7}$ $m = (-color(red)(3))/color(blue)(-7) = 3/7$

Answer 2 · 2017-11-27T16:03:21

$S l o p e = m = \frac{3}{7}$ $Slope = m = 3/7$

Explanation:

$7 y - 3 x = 21$ $7y-3x=21$

This equation is in standard form $a x + b y = c$ $ax+by=c$

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

Begin by rearranging the equation to equal $y$ $y$

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

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

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

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

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

$\frac{7 y}{7} = \frac{3 x}{7} + \frac{21}{7}$ $color(blue)((7y)/7)=(3x)/color(blue)(7)+21/color(blue)7$

$y = \frac{3}{7} x + 3$ $y=3/7x+3$

Now the equation is in slope-intercept form

$y = \frac{3}{7} x + 3$ $y=color(green)(3/7)x+3$

$y = m x + b$ $y=color(green)mx+b$

Remember, $m$ $m$ is the slope

$S l o p e = m = \frac{3}{7}$ $Slope = m = 3/7$

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

2 Answers

Explanation:

Explanation:

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