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Finding the Slope of a Line from an Equation - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To find the slope of a line given the equation of the line, first write it in slope-intercept form. Use inverse operations to solve for y so that it is written as y=mx+b. Then you can easily see the slope since it is the coefficient of the x variable, or the number in front of x. Remember to include the right sign of the slope.

When you’re asked to find the slope of the line for a given equation, it can be really easy if the line is already in y equals mx plus b form. If you remember when y is all by itself and we have an equation solves for y, the slope is just the coefficient for x, so if I can take this line and solve for y, so that y is isolated, then my slope numbers are going to jump out on me. It’s going to be the co-efficient of x. So let’s do it.

If I want to solve for y, that means get y all by itself, I’m going to subtract x from both sides. I’m going to rewrite this problem down here so I have more space. Okay subtract x from both sides, so that I have -2y equals –x plus 6 and I’m still not quite there yet because y is being multiplied by -2, the opposite of multiplying is to divide.

So I’m going to divide everything by -2, and now I’ll have y= equals -x/-2 becomes +x/2, or you can think of that as 1/2 plus let’s see 6 divide by -2 is -3. Okay so this is the exact same equation just rewritten, I just moved stuff around. I haven’t changed any values, but now I can see that the slope number is whatever the co-efficient of x is, and this one’s kind of tricky because x/2, does that mean the slope is 2? Not quite, the slope is going to be 1/2; I’m going to try to put a little box around it. The slope is the entire co-efficient, there’s a secret x, excuse me a secret 1 in front of x there, so your slope number is not just x/2. It’s not 2, your slope number is 1/2, this is you final answer, slope equals 1/2.

Again the way you can do these problems if you’re given an equation and asked to find the slope, is to get your equation so that it’s solved for y. Put it into y equals mx plus b form, and then the slope number is just the co-efficient in front of x.

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