79 G1.04: Examples 8-14
Additional examples:
Example 8: Find the slope and intercept of the line [latex]y=-2.32x+7.89[/latex]
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The slope is -2.32 and the y-intercept is 7.89.
Example 9: Find the slope and intercept of the line [latex]y=84.4+9.2x[/latex]
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The slope is 9.2 and the y-intercept is 84.4
Example 10: Find the slope and intercept of the line [latex]y=1127-93x[/latex]
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The slope is -93 and the y-intercept is 1127
Example 11: Find the slope and the intercept of the line [latex]y=2178x-114[/latex]
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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)
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[latex]\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}[/latex]
Example 13: Find the formula for the line through (8,5) and (13,17)
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[latex]m=\frac{17-5}{13-8}=\frac{12}{5}=2.4[/latex]
Then, using this slope and the second point: [latex]\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}[/latex]
Example 14: Find the formula for the line through (83.8, 79.9) and (232.7, 63.4)
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[latex]m=\frac{79.9-63.4}{83.8-232.7}=\frac{16.5}{-148.9}=-0.11[/latex]
Then, using this slope and the first point: [latex]\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}[/latex]