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nata0808 [166]
2 years ago
7

Write the equation of the line that passes through the point (-3, 6) and is parallel to the line

Mathematics
2 answers:
denis23 [38]2 years ago
8 0

Answer:

y=\displaystyle\frac{1}{2}x+\displaystyle\frac{15}{2}

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where <em>m</em> is the slope of the line and <em>b</em> is the y-intercept (the value of y when the line crosses the x-axis).
  • Parallel lines always have the same slope (<em>m</em>)

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

y=\displaystyle\frac{1}{2} x+5

From the given equation, we can tell that the slope is \displaystyle\frac{1}{2}. Because parallel lines always have the same slope, the slope of the line we're solving for is therefore \displaystyle\frac{1}{2} as well. Plug this into y=mx+b:

y=\displaystyle\frac{1}{2}x+b

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

y=\displaystyle\frac{1}{2}x+b

We're given that the line passes through the point (-3,6). Plug this into y=\displaystyle\frac{1}{2}x+b and solve for <em>b</em>:

6=\displaystyle\frac{1}{2}(-3)+b\\\\6=\displaystyle\frac{-3}{2}+b\\\\b=\frac{15}{2}

Therefore, the y-intercept is \displaystyle\frac{15}{2}. Plug this back into y=\displaystyle\frac{1}{2}x+b:

y=\displaystyle\frac{1}{2}x+\displaystyle\frac{15}{2}

I hope this helps!

Ugo [173]2 years ago
5 0

Answer:

\because \:l_{1}  \parallel \: l_{2} \\  \therefore m_{1} = m_{2} =  \frac{1}{2}  \\  \frac{y - 6}{x + 3} =  \frac{1}{2} \\ y - 6 =  \frac{1}{2}x + \frac{3}{2} \\ y = \frac{1}{2}x + \frac{3}{2} + 6\\ y = \frac{1}{2}x + \frac{15}{2}

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