Question

Write the equation of a line that passws through the point (1,7) and is perpendicular to y=1/2x-5

Answer 1

Answer:

$y=-2x+5$

Step-by-step explanation:

For one line to be perpendicular to another, their slopes must multiply to -1. So, we really want the line with slope $-1/(1/2) = -2$ that passes through the point $(1, 7)$.

Recall the point-slope form of a line. If you have a point $(x_{1}, y_{1})$ and a slope $m$, the line through that point with the given slope is $y-y_{1}=m(x-x_{1})$. Plugging in our given point and slope gives our line: $y-7=-2(x-1)$(point-slope form).

We can convert this line to slope-intercept form, the most common form by expanding the right side and adding $7$ to get $y$ by itself:

$y-7=-2x+2$

$y=-2x+5$