Write the equation (in slope-intercept form) for the line through the point

Question

Write the equation (in slope-intercept form) for the line through the point  perpendicular to the line .

Answer 1

For a line to be perpendicular to another, the slopes are going to be negative reciprocals of each other. But what does a negative reciprocal mean?

A negative reciprocal is -1 divided by the number. For example: for 8, the negative reciprocal is -1/8.

The slope of the given line is 3, since the equation of the line is given in slope intercept form.

Slope intercept form is: y = m*x + b where m is the slope, or the rate of change of the line, and b is the point where the line crosses the y - axis.

So the line has to be perpendicular to a line with a slope of 3, that means that the slope of the perpendicular line is going to be: -1/3. So for the equation of the line right now, we have y = -x/3 + b.

But, for the value of b, we have to plug in the value of the coordinates that is given to us: (-3, 2)

y = -x/3 + b

2 = (-3)(-1/3) + b

2 = 1 + b

b = 1

That means that the equation of the line that is perpendicular to the line y = 3x - 7 and goes through (-3, 2) is: y = -x/3 + 1