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What is the slope of the line through (-7,-8) and (0,4) ? Choose 1 answer: (A) -(12)/(7) (B) (12)/(7) (c) (7)/(12) (D) -(7)/(12)

What is the slope of the line through (−7,−8)(-7,-8) and (0,4)(0,4)?\newlineChoose 11 answer:\newline(A) −127-\frac{12}{7}\newline(B) 127\frac{12}{7}\newline(C) 712\frac{7}{12}\newline(D) −712-\frac{7}{12}

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Full solution

Q. What is the slope of the line through (−7,−8)(-7,-8) and (0,4)(0,4)?\newlineChoose 11 answer:\newline(A) −127-\frac{12}{7}\newline(B) 127\frac{12}{7}\newline(C) 712\frac{7}{12}\newline(D) −712-\frac{7}{12}
  1. Identify slope formula: Identify the slope formula.\newlineThe slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:\newlineSlope = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}
  2. Substitute given points: Substitute the given points into the slope formula.\newlineWe have the points (−7,−8)(-7, -8) and (0,4)(0, 4). Let's assign these values to the formula:\newlinex1=−7x_1 = -7, y1=−8y_1 = -8, x2=0x_2 = 0, y2=4y_2 = 4.\newlineSlope = 4−(−8)0−(−7)\frac{4 - (-8)}{0 - (-7)}
  3. Calculate change in y: Calculate the change in y (rise).Change in y=y2−y1=4−(−8)=4+8=12\text{Change in } y = y_2 - y_1 = 4 - (-8) = 4 + 8 = 12
  4. Calculate change in x: Calculate the change in x (run). \newlineChange in x = x2−x1=0−(−7)=0+7=7x_2 - x_1 = 0 - (-7) = 0 + 7 = 7
  5. Calculate slope: Calculate the slope using the changes in y and x.\newlineSlope = Change in yChange in x=127 \frac{\text{Change in } y}{\text{Change in } x} = \frac{12}{7}
  6. Determine correct answer: Determine the correct answer from the given options.\newlineThe calculated slope is 127\frac{12}{7}, which corresponds to option (B).

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