Question

Find the equation of the line that is perpendicular to the line y =- 1/3 x-1 and passes through the point (1, 5)? Justify how you knew what slope to use for step 1. Show ALL work needed to complete this problem

Answer 1

To find the other line's slope, take the "opposite reciprocal"

For example, if the slope is -1/3, you change the negative sign to positive and you take the reciprocal.

-1/3 --> +3/1

The slope of the perpendicular will be positive 3. To find the equation that passes through the point (1,5), substitute the x and y values into the equation y=mx+b and solve for b, because you know the slope already, now you have to find the y-intercept (the b in the equation).

5=3(1)+b

5=3+b

5-3= 3-3+b

2=b

The equation of the perpendicular line is y=3x+2