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What is the slope of the line? $\newline$ $-4x+7=2y-3$ $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{1}{2}$ $\newline$ (B) $-\frac{1}{3}$ $\newline$ (C) $-3$ $\newline$ (D) $-2$

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Multiply polynomials

Full solution

Q. What is the slope of the line?

\newline

-4x+7=2y-3

\newline

Choose

1

answer:

\newline

(A)

-\frac{1}{2}

\newline

(B)

-\frac{1}{3}

\newline

(C)

-3

\newline

(D)

-2

Rearrange equation: Rearrange the equation to solve for $y$ , making it easier to identify the slope. Start by adding $4x$ to both sides to isolate terms involving $y$ on one side. $\newline$ $-4x + 7 + 4x = 2y - 3 + 4x$ $\newline$ $7 = 2y - 3 + 4x$
Simplify and isolate: Next, simplify and isolate $2y$ by moving the constant term to the other side. Add $3$ to both sides. $\newline$ $7 + 3 = 2y + 4x$ $\newline$ $10 = 2y + 4x$
Subtract to isolate: Now, subtract $4x$ from both sides to fully isolate the $2y$ term. $\newline$ $10 - 4x = 2y$
Divide to solve: Divide every term by $2$ to solve for $y$ . $\newline$ $(10 - 4x)/2 = y$ $\newline$ $5 - 2x = y$
Identify slope: From the equation $y = 5 - 2x$ , identify the coefficient of $x$ , which represents the slope of the line. $\newline$ Slope = $-2$

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