How can you solve for b in y=mx+b?

2 Answers
May 10, 2018

b tends to be the y intercept which can be worked out given that you have the gradient and any coordinate of a point on that line. Just substitute them values in, rearrange to make b the subject which will give you the y-intercept (b).

Explanation:

For example:

y = 2x + b

and you know that the coordinate (5, 2) lies on this function. Simple substitute them in and work out your value of b.

2 = 2(5) + b
b = 2-10
b = -8

Therefore your final equation will be: y = 2x - 8

May 10, 2018

b=y-mx

Explanation:

Given: y=mx+b

The objective is to have just 1 of b and for this to be on one side of the equals and everything else on the other side.

To get b on its own subtract color(red)(mx) from both sides

color(green)(ycolor(white)("d")=color(white)("d")mx+b color(white)("dddd")-> color(white)("dddd")ycolor(red)(-mx)color(white)("d")=color(white)("d")ubrace(mxcolor(red)(-mx))+b)
color(white)("dddddddddddddddddddddddddddddddddd.")darr

color(green)(color(white)("ddddddddddddddd")->color(white)("dddd")y-mxcolor(white)("d")=color(white)("dddd")0color(white)("ddd")+b)

b=y-mx