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Difficulty: EasySlope of a Line

What is the slope of the line represented by the equation 5x+3y=−125x + 3y = -12 in the standard (x,y)(x, y) coordinate plane?

  1. A
    53\frac{5}{3}
  2. B
    −35-\frac{3}{5}
  3. −53-\frac{5}{3}Answer
  4. D
    35\frac{3}{5}
  5. E
    −5-5

Answer

−53-\frac{5}{3}
The correct answer is found by converting the standard form equation 5x+3y=−125x + 3y = -12 into slope-intercept form (y=mx+by = mx + b). Subtracting 5x5x from both sides gives 3y=−5x−123y = -5x - 12. Dividing both sides by 33 yields y=−53x−4y = -\frac{5}{3}x - 4. Thus, the slope of the line is the coefficient of xx, which is −53-\frac{5}{3}.

Step-by-Step Solution

1
Start with the given equation in standard form.
5x+3y=−125x + 3y = -12
Identify the equation to be transformed.
2
Subtract 5x5x from both sides of the equation to isolate the term containing yy.
3y=−5x−123y = -5x - 12
Move the xx term to the right side of the equation.
3
Divide every term in the equation by 33 to solve for yy in slope-intercept form (y=mx+by = mx + b).
y=−53x−4y = -\frac{5}{3}x - 4
Isolate yy so that the coefficient of xx represents the slope.
4
Identify the coefficient of xx, which is the slope mm.
m=−53m = -\frac{5}{3}
In the form y=mx+by = mx + b, the slope is mm.

Key Concept

To find the slope of a line from its linear equation, rewrite the equation in slope-intercept form, y=mx+by = mx + b, where mm represents the slope.
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Topics

Slope of a Line

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