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# How to Graph a Line using y=mx+b - Problem 3

###### 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 graph a line using the standard form of a line, find the x and y-intercepts. To find the x-intercept, substitute in 0 for y and solve for x. The resulting value for x will be the x-intercept, of the point on the x-axis where the graph of the line will pass. To find the y-intercept, substitute in 0 for x and solve for y. The resulting value for y will be the y-value of y-intercept, or the point on the y-axis where the graph of the line will pass.

Here I'm asked to graph an equation that's given to me in standard form. A lot of people choose to graph problems like these by finding the x and y intercepts and that's absolutely a valid method. The way you would do that is substitute in 0 for x to find the y intercept. Substitute in 0 for y to find the x intercept and then connect those two points.

I want to show you another way using Slope-Intercept. It's my personal favourite method because for me it's the quickest. Even though this equation is not in Slope-Intercept form, I can get it into Slope-Intercept form without too much difficulty. Slope-Intercept form remember look like this where y is all by itself. So first thing I need to do is get rid of this -2x by adding 2x to both sides of the equal sign, so I'll have -4y equals +2x plus 8.

Then since I want y all by itself, I'm going to divide by -4 all the way across, so now I'll have y equals 2 over -4 reduces to -1/2 and then 8 over -4 reduces to -2. This is the same equation as that original one only written in a different form and I like this form because I can graph it using Slope-Intercept.

Here is how. My first dot will go at -2 on the y axis because that's the y intercept. From there I'm going to count the slope which is going to be down 1, right 2 because it's negative. I'll show you what I mean. Our first dot is going to go at -2 on the y axis, so here we go y axis -2. From there, I need to show a negative slope, so instead of going up 1 over 2, I'm going to go down 1 over 2. I'm going to draw a couple points in this direction so I can make sure my line is correct when I get the ruler up there.

You could also draw a negative slope form here by going up 1, but then to the left 2. This is the same slope. It's still a slope of -1/2. I have that constant ratio all the way across my line. All I have to do left is connect the little points and then stick arrows on the end. Connect them like so, make a sound effect if you want to, and then stick arrows on the end.

Okay that's an A+ graph that I did pretty easily. You could have used intercepts to solve this problem, but my personal preference, the way that I make the fewest errors, is by putting into y equals mx plus b form and counting the slope after I start at the y intercept.

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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.

Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”

Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”

You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”

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