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nlexa [21]
2 years ago
5

Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x

Mathematics
1 answer:
egoroff_w [7]2 years ago
8 0

Answer:

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

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

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

y = 1 -2x

Rearrange into slope-intercept form:

y = -2x+1

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of \displaystyle\frac{1}{2}. Plug this into y=mx+b:

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

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

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

Plug in the given point (1,3) and solve for <em>b</em>:

3=\displaystyle\frac{1}{2} *1+b\\\\b=\displaystyle \frac{5}{2}

Therefore, the y-intercept is \displaystyle \frac{5}{2}. Plug this back into y=\displaystyle\frac{1}{2} x+b:

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

I hope this helps!

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