16.4: G1.04- Examples 8-14

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Additional examples:

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

[reveal-answer q=”429582″]Show Answer[/reveal-answer]
[hidden-answer a=”429582″]The slope is -2.32 and the y-intercept is 7.89.[/hidden-answer]

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

[reveal-answer q=”185443″]Show Answer[/reveal-answer]
[hidden-answer a=”185443″]The slope is 9.2 and the y-intercept is 84.4[/hidden-answer]

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

[reveal-answer q=”191120″]Show Answer[/reveal-answer]
[hidden-answer a=”191120″]The slope is -93 and the y-intercept is 1127[/hidden-answer]

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

[reveal-answer q=”383183″]Show Answer[/reveal-answer]
[hidden-answer a=”383183″]The slope is 2178 and the y-intercept is -114.[/hidden-answer]

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

[reveal-answer q=”695808″]Show Answer[/reveal-answer]
[hidden-answer a=”695808″] $\begin{align}&y-{{y}_{0}}=m(x-{{x}_{0}})\\&y-112.7=-6.2(x-87.2)\\&y-112.7=-6.2x+540.64\\&y-112.7+112.7=-6.2x+540.64+112.7\\&y=-6.2x+653.34\end{align}$ [/hidden-answer]

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

[reveal-answer q=”272460″]Show Answer[/reveal-answer]
[hidden-answer a=”272460″]

$m=\frac{17-5}{13-8}=\frac{12}{5}=2.4$

Then, using this slope and the second point: $\begin{align}&y-{{y}_{0}}=m(x-{{x}_{0}})\\&y-17=2.4(x-13)\\&y-17=2.4x-31.2\\&y-17+17=2.4x-31.2+17\\&y=2.4x-14.2\end{align}$

[/hidden-answer]

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

[reveal-answer q=”867398″]Show Answer[/reveal-answer]
[hidden-answer a=”867398″]

$m=\frac{79.9-63.4}{83.8-232.7}=\frac{16.5}{-148.9}=-0.11$

Then, using this slope and the first point: $\begin{align}&y-{{y}_{0}}=m(x-{{x}_{0}})\\&y-79.9=-0.11(x-83.8)\\&y-79.9=-0.11x+9.218\\&y-79.9+79.9=-0.11x+9.218+79.9\\&y=-0.11x+89.118\\\end{align}$

[/hidden-answer]

Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution