A straight line has the equation three 𝑦 minus 15𝑥 minus 12 is equal to zero. What is the slope of the line?
We recall first that the slope of a line is the measure of how steep it is. We often denote the slope using the letter 𝑚. And it means that for every one unit the line moves to the right, it moves 𝑚 units up. If the value of 𝑚 is positive, then the line will slope upwards from left to right, whereas if 𝑚 is negative, the line will slope downwards.
To answer this question, we’re going to recall the slope-intercept form of the equation of a straight line 𝑦 equals 𝑚𝑥 plus 𝑏, where the value of 𝑚, the coefficient of 𝑥, gives the slope of the line and the value of 𝑏, the constant term, gives the 𝑦-intercept. The equation of our line three 𝑦 minus 15𝑥 minus 12 equals zero has not been given in this form, but we can rearrange it to bring it into the slope-intercept form. We want to make 𝑦 the subject, so leave 𝑦 on its own on one side of the equation.
The first step is to isolate the 𝑦-terms, so we can add 15𝑥 and 12 to each side, giving three 𝑦 equals 15𝑥 plus 12. The next step is to divide both sides of the equation by three, giving 𝑦 is equal to five 𝑥 plus four. And now we have an equivalent form of the equation of the straight line, and it’s in the slope-intercept form. We can therefore read off the slope of the line. It’s the coefficient of 𝑥, which is five. If we’re interested, we can also see that the 𝑦-intercept of this line is positive four.
So by rearranging the equation of the straight line into the slope-intercept form, we’ve found that the slope of the line three 𝑦 minus 15𝑥 minus 12 equals zero is five, which means for every one unit the line moves to the right, it will move five units up.