Video Transcript
What is the equation of a line that contains the point one, five and has a 𝑦-intercept of two?
Here, we remember the slope form of a line. 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑏 is the 𝑦-intercept and 𝑚 is the slope of the line. If we add the point one, five and our 𝑦-intercept equals two, we’ll plug that information in the form 𝑦 equals 𝑚𝑥 plus 𝑏. We’ll plug in two for the 𝑦-intercept, our 𝑏-variable, and one of our coordinate pairs. We have 𝑥 equals one and 𝑦 equals five. That means we can say five equals the slope of the line times one plus two.
We wanna solve for 𝑚. 𝑚 times one equals 𝑚. We now have five equals 𝑚 plus two. So we subtract two from both sides. And we see that three equals 𝑚. And we can flip that to say 𝑚 equals three. Now that we have both our slope and our 𝑦-intercept, we’re ready to write an equation for this line. 𝑦 equals the slope, three, times 𝑥 plus the 𝑦-intercept, which is two.
The equation of the line given this point and this 𝑦-intercept would be 𝑦 equals three 𝑥 plus two.
