Video: Finding the 𝑦-Intercept of a Straight Line Equation

Find the coordinates of the point where 𝑦 = 4𝑥 +12 intersects the 𝑦-axis.

01:30

Video Transcript

Find the coordinates of the point where 𝑦 equals four 𝑥 plus 12 intersects the 𝑦-axis.

So in this question, we’re given the equation of a straight line in slope-intercept form. And we’re asked for the coordinates of the point where it intersects the 𝑦-axis. What this question is checking then is do we understand slope-intercept form and what the different parts of the equation represent. Remember that slope-intercept form is 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑐 represents the 𝑦-intercept of the straight line, which is what we’re looking for here. The 𝑦-intercept is the point where the line intersects the 𝑦-axis. So we can see by comparing the general form and the specific straight line that we have, the value of 𝑐 here is 12.

But the question doesn’t just ask us for the value of 𝑐; it asks us for the coordinates of this point. So the 𝑦-intercept remember is a point on the 𝑦-axis. We’ve just worked out its 𝑦-coordinate; it’s this value of 12. To work out the 𝑥-coordinate, we just need to remember that at every point on the 𝑦-axis the 𝑥-coordinate is zero. You could perhaps see this more clearly by picturing what the graph would look like as I’ve done here. So the coordinates of this point then are going to be zero, 12. And that is our final answer to this question.

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