# Question Video: Finding the Slope of a Line Given Its Equation Mathematics

A straight line has the equation 3π¦ β 15π₯ β 12 = 0. What is the slope of the line?

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### Video Transcript

A straight line has the equation three π¦ minus 15π₯ 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 π. And it means that for every one unit the line moves to the right, it moves π units up. If the value of π is positive, then the line will slope upwards from left to right, whereas if π is negative, the line will slope downwards.

To answer this question, weβre going to recall the slope-intercept form of the equation of a straight line π¦ equals ππ₯ plus π, where the value of π, the coefficient of π₯, gives the slope of the line and the value of π, the constant term, gives the π¦-intercept. The equation of our line three π¦ minus 15π₯ 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 π¦ the subject, so leave π¦ on its own on one side of the equation.

The first step is to isolate the π¦-terms, so we can add 15π₯ and 12 to each side, giving three π¦ equals 15π₯ plus 12. The next step is to divide both sides of the equation by three, giving π¦ is equal to five π₯ plus four. And now we have an equivalent form of the equation of the straight line, and itβs in the slope-intercept form. We can therefore read off the slope of the line. Itβs the coefficient of π₯, which is five. If weβre interested, we can also see that the π¦-intercept of this line is positive four.

So by rearranging the equation of the straight line into the slope-intercept form, weβve found that the slope of the line three π¦ minus 15π₯ minus 12 equals zero is five, which means for every one unit the line moves to the right, it will move five units up.