Question Video: Finding the Equation of a Graph Given a Point and the Slope Mathematics

Video Transcript

Find in point-slope form the equation of the graph with slope four that passes through the point two, negative three.

The point-slope form equation is 𝑦 minus 𝑦 one equals 𝑚 times 𝑥 minus 𝑥 one, where the point is 𝑥 one 𝑦 one and the slope is 𝑚. Our point given was two, negative three and the slope was equal to four, so let’s go ahead and take our equation and plug these in.

So we have 𝑦 minus 𝑦 one. So 𝑦 minus negative three equals 𝑚 which is four times 𝑥 minus 𝑥 one, so 𝑥 minus two. Now let’s simplify the left-hand side, because the two negatives will turn into a positive. So in point slope form, the equation of this graph would be 𝑦 plus three equals four times 𝑥 minus two. And again, this is in point-slope form.