A straight line has the equation negative 15𝑥 plus three 𝑦 minus 12 equals zero. What is the slope of the line?
The most efficient way to answer this question is to rearrange the equation we’ve been given into the slope–intercept form. That is, 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚, the coefficient of 𝑥, represents the slope of the line and 𝑏, the constant term, represents its 𝑦-intercept. So if we take the equation we’ve been given and rearrange it to make 𝑦 the subject, we’ll then be able to read off the slope and, if we wish, the 𝑦-intercept.
The first step then is to isolate the 𝑦-term, which we can do by adding both 15𝑥 and 12 to each side of this equation. On the left-hand side, we’re left with three 𝑦, and on the right-hand side, we have 15𝑥 plus 12. So the equation has become three 𝑦 is equal to 15𝑥 plus 12. We can then divide both sides of the equation by three. On the left-hand side, three 𝑦 divided by three is equal to 𝑦. On the right-hand side, 15𝑥 divided by three is five 𝑥 and positive 12 divided by three is four. So we have 𝑦 is equal to five 𝑥 plus four.
This equation is now in the slope–intercept form of the equation of a straight line. We can determine its slope by considering the coefficient of 𝑥, which we see is five. Although it’s not required in this question, we can also see that the 𝑦-intercept of the line is positive four. So by rearranging the equation of this straight line into the slope–intercept form 𝑦 equals 𝑚𝑥 plus 𝑏, we found that the slope of the line with equation negative 15𝑥 plus three 𝑦 minus 12 equals zero is five.