# 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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## 2 Answers

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 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 at 22:23
Whoops, my mistake. Thank you! – user60161 Feb 19 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 at 22:25

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