# Thread: Finding X in y = mx + b equations

1. ## Finding X in y = mx + b equations

Hello:

I am doing a math worksheet that I was given by my teacher, the sheet is full of slope problems. y = mx + b. You are given two points:

Example:

(4,1) (5,3) and you have to find what Y = and my answer was Y = 2x - 7
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There are two equations on here where it says X = for the answer instead. The two points are (4,1) and (4,13).

Hopefully I am not being too confusing, thanks in advance for any help.

2. Originally Posted by CzWJF41
Hello:

I am doing a math worksheet that I was given by my teacher, the sheet is full of slope problems. y = mx + b. You are given two points:

Example:

(4,1) (5,3) and you have to find what Y = and my answer was Y = 2x - 7
Hi there

$\displaystyle m = \frac{y_2-y_1}{x_2-x_1} = \frac{3-1}{5-4} = \frac{2}{1} = 2$

with

$\displaystyle y = mx + b$

is now

$\displaystyle y = 2x + b$

so far so good.

Now use either point to find b. Using $\displaystyle (4,1)$ gives

$\displaystyle 1 = 2\times 4 + b$

$\displaystyle b=-7$ so $\displaystyle y = 2x -7$

Good news for you!

3. $\displaystyle (4,1)$ and $\displaystyle (4,13)$ are on the line $\displaystyle x = 4$.

You may sketch these two points in a coordinate system and construct a line through them, and as it can be seen this line is actually perpendicular to the x-axis.

That means, all points designated as (4, a) (a can be any real number) are on the line because they all satisfy the condition that x = 4, given that there is nothing required for y.