Passing through (3,5) and perpendicular to the line whose equation is y=1/7x+4, point-intercept form

Question

Original question. Use the given conditions to write an equation for the line in point-slope and slope-intercept form. Question above is part b of the original question.

Answer 1

Hello Shatanna!

So the slope of a perpendicular line is the negative reciprocal of the slope of the original line (a reciprocal is essentially flipping the fraction, switching the numerator and the denominator). So IF the slope of the original line was 3/2, the slope of the perpendicular line would be -2/3.

In our example the slope was initially 1/7, so the new slope would be -7/1, or just -7.

Point-slope form of a line has a general form of (y-y₁)=m(x-x₁), where m is the slope and (x₁, y₁) is a given point on the line. Point-Slope form is usually the easiest form of the equation to figure out.

So in the problem you gave, Point-Slope from would be (y-5)=(-7)(x-3).

Slope-intercept form is the most common form of the equation for a line, and the general form is y=mx+b, where m is the slope and b is the y-intercept. To arrive there from Point-Slope form we first distribute the -7, giving us:
(y-5)=-7x+21. Then we add 5 to each side of the equation and arrive at y=-7x+26.

I hope that this helps!