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Nitella [24]
3 years ago
10

What is the slope of a line that is parallel to the line whose equation is 0.5x-5y=9

Mathematics
2 answers:
Tems11 [23]3 years ago
6 0

0.5x - 5y = 9

<u>Make y the subject:</u>

5y = 0.5x - 9

y = 0.1x - 1.8

Match equation with y = mx + b

m = slope = 0.1

Parallel Slope = 0.1

Answer: The slope of the parallel line is 0.1

vovikov84 [41]3 years ago
3 0

The slopes of parallel line are the same.

We have: 0.5x - 5y = 9

Let's transform to slope-intercept form y = mx + b

0.5x - 5y = 9 |-0.5x

-5y = -0.5x + 9 |:(-5)

y = 0.1x - 1.8

Your answer is m = 0.1

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Thus,

\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}

thus, BC = 7.5

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In the above diagram,

\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}

Thus, from the theorem of similar triangles,

\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}

solving for y, we have

\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}

thus, YC = 10.

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