Question Video: Finding the Slope and 𝑦-Intercept of a Linear Function Mathematics • 8th Grade

Video Transcript

Calculate the slope 𝑚 and the 𝑦-intercept 𝑏 for the function five 𝑦 equals 10𝑥 plus 30.

If we can get an equation into slope intercept form, where 𝑦 is isolated and it’s equal to 𝑚𝑥 plus 𝑏, 𝑚 is your slope and 𝑏 is your 𝑦-intercept.

So looking at the equation we have, we’re almost there. We just need to get 𝑦 by itself. And five is being multiplied to 𝑦. So in order to get rid of five, we need to divide by five. So we would need to divide by five to both sides of our equation. On the left-hand side, the fives will cancel. And on the right-hand side, we need to take 10𝑥 and divide by five, and 30 divide by five because we’re dividing the entire right side by five.

It can also be written like this. So we’re again gonna take 10𝑥, divide by five, and 30, and divide by five. 10𝑥 divided by five is two 𝑥, and 30 divided by five is six. So now we are in slope intercept form, 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is two, also known as our slope, and six is 𝑏, our 𝑦-intercept.

Again, our slope 𝑚 is equal to two. Or, that can be written as two over one because usually a slope is written as a fraction because slope is rise over run. And the 𝑦-intercept, 𝑏, is equal to six.