# Finding the coordinates of the point where each line crosses the $y$-axis

I have a problem like this:

Give the coordinates of the point where each line crosses the $y$-axis.

Then it gives me an equation in slope-intercept form, here is an example:

$y=3x+4$

Would I just use the $y$-intercept ($4$) and write down the answer as $(0,4)$?

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Yes, that's correct. The "b" value in the slope-intercept form: $$y = mx + b$$ denotes the y-coordinate at $x = 0$, hence, the y-intercept is given $b$, meaning the point of intersection of the line and the y-axis is the point $(0, b)$.

In your example, $$y = 3x + 4,$$ slope = $m = 3$, and $b = 4$ is the y-value at which the line "intercepts" the y-axis (y axis: $x = 0$). Hence $(0, 4)$ is the point of intersection.

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Ahh thank you! So lets say if I have a problem like y=(1/2)x, would the answer just be (0,0) since the "b" value would just be interpreted as 0? –  user60161 Feb 19 '13 at 22:22
@user60161: that is correct, assuming by 1/2x you meant (1/2)x not 1/(2x). Please use parentheses when using slashes for division. –  Ross Millikan Feb 19 '13 at 22:23
Whoops, my mistake. Thank you! –  user60161 Feb 19 '13 at 22:25
user60161 yes, assuming you mean $y = (1/2)x$, then $b = 0$, hence the point of intersection of the line with the y-axis is the origin $(0,0)$ –  amWhy Feb 19 '13 at 22:25

In general you could always just plug in $x=0$ and solve, no matter what form its in

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