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Writing Linear Functions

Writing Linear Functions 1.11 - Solution

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To see if Ron-Jon is correct or not, we'll determine the slope of the line ourselves. We find the slope of a line by dividing the vertical change by the horizontal change between two points on the line. We can use the slope formula for this: m=y2y1x2x1. m=\dfrac{y_2-y_1}{x_2-x_1}. Thus, we need to identify two points on the line.

The two points on the line are given as (0,0)({\color{#0000FF}{0}},{\color{#0000FF}{0}}) and (-3,5)({\color{#009600}{\text{-}3}},{\color{#009600}{5}}). When we substitute them into the formula we get: m=50-30=5-3=-53 m=\dfrac{{\color{#009600}{5}}-{\color{#0000FF}{0}}}{{\color{#009600}{\text{-}3}}-{\color{#0000FF}{0}}}=\dfrac{5}{\text{-}3}=\text{-}\frac{5}{3} It's a negative slope, because the line is sloping downward. The mistake Ron-Jon made was in calculating the slope. The points did not line up accordingly. The coordinates must be put into the slope formula in the correct order.