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

A straight line has the equation 3𝑦 βˆ’ 15π‘₯ βˆ’ 12 = 0. What is the slope of the line?

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Video Transcript

A straight line has the equation three 𝑦 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‘š. And it means that for every one unit the line moves to the right, it moves π‘š units up. If the value of π‘š is positive, then the line will slope upwards from left to right, whereas if π‘š 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 π‘šπ‘₯ plus 𝑏, where the value of π‘š, the coefficient of π‘₯, 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 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 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 15π‘₯ and 12 to each side, giving three 𝑦 equals 15π‘₯ plus 12. The next step is to divide both sides of the equation by three, giving 𝑦 is equal to five π‘₯ 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 π‘₯, 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 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.

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