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Finding the Slope of a Line from an Equation  Problem 2
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 slopeintercept 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 coefficient 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 coefficient 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 coefficient, 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 coefficient in front of x.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Sample Problems (7)
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Finding the Slope of a Line from an Equation
Problem 1 16,164 viewsFind the slope of the line:
y = ⅔x + 6 
Finding the Slope of a Line from an Equation
Problem 2 13,390 viewsFind the slope of the line:
x − 2y = 6 
Finding the Slope of a Line from an Equation
Problem 3 10,467 viewsFind the slope of the line:
y = 4 
Finding the Slope of a Line from an Equation
Problem 4 9,269 viewsFind the slope of the line:
x = 2 
Finding the Slope of a Line from an Equation
Problem 5 1,791 views 
Finding the Slope of a Line from an Equation
Problem 6 840 views 
Finding the Slope of a Line from an Equation
Problem 7 876 views
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