Question

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

Answer 1

Answer:

slope = 2

Step-by-step explanation:

Answer 2

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:

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