Write, in the form 𝑦 equals 𝑚𝑥 plus 𝑐, the equation of the line of slope eight over 11 or eight elevenths that meets the 𝑦-axis at the point zero, five.
So 𝑦 equals 𝑚𝑥 plus 𝑐 is actually the general form for a straight line, where 𝑚 is actually the slope of our line, so it’s how steep it is, and 𝑐 is actually the 𝑦-intercept, so this is where it crosses the 𝑦-axis. But what I’ve done to actually help us solve this problem and understand really where it comes from is draw a little sketch of our line.
Well, first of all, we can see that actually our line crosses the 𝑦-axis at five. And we got that because it says that it meets the 𝑦-axis at the point zero, five, so 𝑥-coordinate zero, 𝑦-coordinate five. So therefore, we can say that 𝑐 is gonna be equal to five because our 𝑦-intercept is five. And we know that 𝑚 is going to be equal to eight elevenths or eight over 11. That’s because it tells us that the slope is eight over 11. But what does this actually mean?
Well, what it means in practice is that our line is gonna go up eight units for every 11 units it goes along. So therefore, the slope is the change in 𝑦 divided by the change in 𝑥, so eight over 11 or eight elevenths.
Okay, great! So we’ve now got these, let’s actually substitute them back into 𝑦 equals 𝑚𝑥 plus 𝑐. So therefore, when we actually substitute these back in, we can say that the equation of the line of slope eight over 11 or eight elevenths that meets the 𝑦-axis at the point zero, five is 𝑦 equals eight elevenths 𝑥 plus five. And that’s in the form 𝑦 equals 𝑚𝑥 plus 𝑐.