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Study Guides > Mathematics for the Liberal Arts

G1.04: Examples 8-14

Additional examples:

Example 8: Find the slope and intercept of the line y=−2.32x+7.89y=-2.32x+7.89

Answer: The slope is -2.32 and the y-intercept is 7.89.

Example 9: Find the slope and intercept of the line y=84.4+9.2xy=84.4+9.2x

Answer: The slope is 9.2 and the y-intercept is 84.4

Example 10: Find the slope and intercept of the line y=1127−93xy=1127-93x

Answer: The slope is -93 and the y-intercept is 1127

Example 11: Find the slope and the intercept of the line y=2178x−114y=2178x-114

Answer: The slope is 2178 and the y-intercept is -114.

Example 12 Find the formula for the line with slope -6.2 through the point (87.2, 112.7)

Answer: \begin{align}&y-{{y}_{0}}=m(x-{{x}_{0}})\\&y-112.7=-6.2(x-87.2)\\&y-112.7=-6.2x+540.64\\&y-112.7+112.7=-6.2x+540.64+112.7\\&y=-6.2x+653.34\end{align}

Example 13: Find the formula for the line through (8,5) and (13,17)

Answer: m=17−513−8=125=2.4m=\frac{17-5}{13-8}=\frac{12}{5}=2.4 Then, using this slope and the second point:   \begin{align}&y-{{y}_{0}}=m(x-{{x}_{0}})\\&y-17=2.4(x-13)\\&y-17=2.4x-31.2\\&y-17+17=2.4x-31.2+17\\&y=2.4x-14.2\end{align}

Example 14: Find the formula for the line through (83.8, 79.9) and (232.7, 63.4)

Answer: m=79.9−63.483.8−232.7=16.5−148.9=−0.11m=\frac{79.9-63.4}{83.8-232.7}=\frac{16.5}{-148.9}=-0.11 Then, using this slope and the first point: \begin{align}&y-{{y}_{0}}=m(x-{{x}_{0}})\\&y-79.9=-0.11(x-83.8)\\&y-79.9=-0.11x+9.218\\&y-79.9+79.9=-0.11x+9.218+79.9\\&y=-0.11x+89.118\\\end{align}

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