Question

write an equation of the line that passes through the given point and is perpendicular to (3,-7), y=-1/5x+1

Answer 1

Remember that perpendicular lines have a slope equal to the negative reciprocal of the slope of the line they are perpendicular to. So, let's find that negative reciprocal.

In this, case we can find the negative reciprocal by dividing -1 by the slope:

$-\dfrac{1}{- \frac{1}{5}} = \dfrac{-1}{1} \cdot \dfrac{1}{- \frac{1}{5}} = -1 \cdot -5 = 5$

The slope of the perpendicular line is 5. Now, we have a point on the line and the slope of the line. Thus, we can use the point-slope formula, which is:

$(y - y_1) = m(x - x_1)$

• $m$ is the slope of the line
• $(x_1, y_1)$ is a point on the line

Thus, the equation of our new line would be:

$(y + 7) = 5(x - 3)$

$y+ 7 = 5x - 15$

$y = 5x - 22$

The equation would be y = 5x - 22.