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ikadub [295]
3 years ago
15

74. What is the slope of the line 6x – 3y = 54 ?.

Mathematics
2 answers:
Nataly_w [17]3 years ago
4 0

Answer:

slope = 2

Step-by-step explanation:

Molodets [167]3 years ago
3 0

Answer:

m=2

Step-by-step explanation:

- Before beginning, I'm going to show the guideline for slope-intercept form for linear equations:

· Slope-Intercept Form: y=mx+b

  • m= slope; the rotation of the line
  • b= the line's y-intercept; where the line hits the y-axis.

· Both m and b are constant integers whose value ranges from -∞ ⇒ ∞, all real numbers.

· y and x are values that depend on each other's value; (x,y) is how you would see them written on a number line.

- With this in mind, let's look at our current equation.

6x-3y=54

- It seems that our equation is not in a form that could easily show us what it's rotation is, slope, or where it hits the y-axis, so we're going to have to rearrange our equation so that it follows the slope-intercept guideline shown above.

6x-3y=54\\6x-3y+(-6x)=54+(-6x)

  • My first step was to move any values that are neither being multiplied nor divided by y to the other side of the equation. In this case, 6x is being added to -3y, so by adding the reciprocal of 6x to both sides, I can move it to the other side.

6x-3y+(-6x)=54+(-6x)\\-3y=-6x+54

  • Now our equation is starting to look somewhat like the guideline for slope-intercept form; all we need to do now is get rid of the -3 next to the y by dividing.

-3y=-6x+54\\\frac{-3y}{-3}=\frac{-6x+54}{-3}\\y=\frac{-6x}{-3}+\frac{54}{-3}

  • Almost there. All that's left is simplification and we're done! -3 goes into -6 two times, and -3 goes into 54 negative eighteen times, so our final, simplified equation is:

y=2x-18

  • By looking at our guideline, y=mx+b where m is slope and b is the y-intercept, we can determine that:

The slope of 6x-3y=54 is 2.

Uninterrupted Work:

6x-3y=54\\6x-3y+(-6x)=54+(-6x)\\-3y=-6x+54\\\frac{-3y}{-3}=\frac{-6x+54}{-3}\\y=\frac{-6x}{-3}+\frac{54}{-3}\\y=2x-18\\m=2

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