Algebra - collinear points, perpendicular line question.?

Question

What is the equation of the line through the origin that is perpendicular to the line y = 1/2x + 1.

Can you also please tell me how to work out how to do these step by step, maybe also how to find parallel line equations, step by step. Thanks.

Answer 1

this is the linear equation in "slop-intercept" form: y = mx + b. to get the equation for your unknown line, you have to obtain the values for m and b.

first lets solve for m. you are told that the unknown line is perpendicular to another line, y=1/2x+1. the slope for the given line is m=1/2. so your unknow m is the negative reciprocal of 1/2. that means that you flip the slope from 1/2 to 2/1 AND you multiply it by a negative. the slope for your unknown line is m= -2/1 and you can simplify that to m= -2.

then, you solve for b. you are also told that your unknown line passes through the origin. that means that the point (0,0) lies on the line. you already know the slope, m= -2 and you are given one point in your unknown line. to solve for b you substitute m= -2, x=0, and y=0.
y = m x +b =
(0)=(-2)*(0)+b, you get b=0. so, your unknown equation is y=-2x+0 and you can rewrite that to y=-2x.

to find a line that is parallel to a given line, you do the same except that the unknown m is NOT the negative reciprocal. the slope stays the same. for example, if you had the same question but instead of perpendicular it said parallel, then the slope would be m=1/2. and your answer would be different. it would be y=1/2x.

i hope i helped =)

Answer 2

The slope of the line given is the coefficient of x, or 1/2. The slope of the perpendicular line would be minus the reciprocal of that, or -2. Therefore the equation of that line is y = -2x + C. The line passes through the origin, meaning at x=0, y=0, therefore C=0.