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What is the slope of the line? 5(y+2)=4(x-3) Choose 1 answer: (A) (2)/(3) (B) (4)/(5) (C) (5)/(4) (D) (3)/(2)

What is the slope of the line?\newline5(y+2)=4(x−3) 5(y+2)=4(x-3) \newlineChoose 11 answer:\newline(A) 23 \frac{2}{3} \newline(B) 45 \frac{4}{5} \newline(C) 54 \frac{5}{4} \newline(D) 32 \frac{3}{2}

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Full solution

Q. What is the slope of the line?\newline5(y+2)=4(x−3) 5(y+2)=4(x-3) \newlineChoose 11 answer:\newline(A) 23 \frac{2}{3} \newline(B) 45 \frac{4}{5} \newline(C) 54 \frac{5}{4} \newline(D) 32 \frac{3}{2}
  1. Rewrite Equation: First, we need to rewrite the equation in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope.5(y+2)=4(x−3)5(y + 2) = 4(x - 3)Distribute 55 to both terms inside the parentheses on the left side and 44 to both terms inside the parentheses on the right side.5y+10=4x−125y + 10 = 4x - 12
  2. Isolate y: Next, we need to isolate yy on one side of the equation to get it into slope-intercept form.\newlineSubtract 1010 from both sides of the equation to move the constant term to the right side.\newline5y=4x−12−105y = 4x - 12 - 10\newline5y=4x−225y = 4x - 22
  3. Solve for y: Now, divide every term by 55 to solve for yy.\newliney=(45)x−225y = \left(\frac{4}{5}\right)x - \frac{22}{5}\newlineThe coefficient of xx, which is 45\frac{4}{5}, is the slope of the line.

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