How to Draw Line Equation

December 23, 2021 Post a Comment

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Are you stuck not knowing how to draw a linear equation without using a calculator? Luckily, drawing a graph of a linear equation is pretty simple! All you need to know is a couple things about your equation and you're good to go. Let's get started!

Steps

1
Make sure the linear equation is in the form y = mx + b. This is called the y-intercept form, and it's probably the easiest form to use to graph linear equations. The values in the equation do not need to be whole numbers. Often you'll see an equation that looks like this: y = 1/4x + 5, where 1/4 is m and 5 is b.^[1]
- m is called the "slope," or sometimes "gradient."^[2]Slope is defined as rise over run, or the change in y over the change in x.
- b is defined as the "y-intercept." The y-intercept is the point at which the line crosses the Y-axis.^[3]
- x and y are both variables. You can solve for a specific value of x, for example, if you have a y point and know the m and b values. x, however, is never merely one value: its value changes as you go up or down the line.
2
Plot the b number on the Y-axis. Your b is always going to be a rational number. Just whatever number b is, find its equivalent on the Y-axis, and put the number on that spot on the vertical axis.
- For example, let's take the equation y = 1/4x + 5. Since the last number is b, we know that b equals 5. Go 5 points up on the Y-axis and mark the point. This is where your straight line will pass through the Y-axis.
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3
Convert m into a fraction. Often, the number in front of x is already a fraction, so you won't have to convert it. But if it isn't, convert it by simply placing the value of m over 1.
- The first number (numerator) is the rise in rise over run. It's how far the line travels up, or vertically.
- The second number (denominator) is the run in rise over run. It's how far the line travels to the side, or horizontally.
- For example:
  - A 4/1 slope travels 4 points up for every 1 point over.
  - A -2/1 slope travels 2 points down for every 1 point over.
  - A 1/5 slope travels 1 point up for every 5 points over.
4
Start extending the line from b using slope, or rise over run. Start at your b value: we know that the equation passes through this point. Extend the line by taking your slope and using its values to get points on the equation.^[4]
- For example, using the illustration above, you can see that for every 1 point the line rises up, it travels 4 to the right. That's because the slope of the line is 1/4. You extend the line indefinitely along both sides, continuing to use rise over run to graph the line.
- Whereas positive-value slopes travel upward, negative-value slopes travel downward. A slope of -1/4, for example, would travel down 1 point for every 4 points it travels to the right.
5

Continue extending the line, using a ruler and being sure to use the slope, m, as a guide. Extend the line indefinitely and you're done graphing your linear equation. Pretty easy, isn't it?^[5]

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Add New Question

Question

What if there is no number for b?

It means the y-intercept is 0. Let's say you have something like y = 5x + 0. The 0 would be taken out because anything plus 0 is itself.
Question

What if the slope is negative?

Then the line will go from top left to bottom right. This is because the rise or run is negative.
Question

How would I graph an equation that is not in slope intercept form? For example: y-2x=0.

Transfer that into a linear equation by taking 2x and reverse the -2x, which brings it to y=2x+0
Question

What if the slope is just x?

Here, the slope is not x, it is the coefficient in front of the x. It doesn't seem like there is one, but remember: When a variable stands a by itself, there is an implied one in front of the variable. So the slope here is actually 1, and you can follow the standard steps for graphing a linear equation.
Question

What do I do if the slope is not a fraction?

Snallison

Community Answer

When the slope is a whole number, (ex. y = 2x + 3), you would put the slope over 1 to make it into a fraction (ex. y = 2/1x + 3). Then you would proceed to graph as normal.
Question

Your explanations of negative slopes is not clear. What do you mean by "...side to side"? If you go left, you get a different line than if you go right. Are there two solutions to negative slopes?

First up, thanks for explaining your concern; we've amended the article to clarify "to the right". By way of explanation, it's as shown in the picture. If positive is one up and one right, then negative will be one down, one right. It means if the line has a slope of -1/4, every one block it goes down, it will go four blocks to the right side-by-side, not randomly. Or, you can also put it as every four blocks it goes right, it goes down one block. You can also put a negative-sloped line as one block up and four blocks left since that's what happens to negative-sloped lines. They travel from top left to bottom right. As always, a linear equation only has one solution per input.
Question

I tried the equation y=2x-3, the answers were (0,-3) (-1,1) (2,1) when their answers were (0,-3) (2,1) (4,5). Can you explain, please?

(4,5) is correct. (-1,1) is not, because if x = -1, 2(-1) - 3 = -5.
Question

Can "b" be a negative number?

Orangejews

Community Answer

Yes. That just means the y-intercept is on the negative (downward) portion of the y-axis.
Question

What if there is no slope, like y= -x+2?

There's always a slope. In this case, it's -1.
Question

How do I graph linear equations when the graph makes a horizontal line or a vertical line?

A horizontal line represents an equation in which there is no x, and y is equal to a constant number, such as y = 3. A vertical line represents an equation in which there is no y, and x is equal to a constant number, such as x = 5.

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About This Article

Article Summary X

To graph a linear equation, start by making sure the equation is in y = mx + b form. Then, plot the b value on the y-axis. Next, convert the m value into a fraction if it's not already by placing it over 1. Once you've done that, start at the point you plotted on the y-axis, and count up the number that's in the numerator of the fraction. From there, count over the number in the denominator, and plot the point on the line. Finally, repeat the process several times, and then connect the points you plotted with a straight line. To learn how to interpret the line you graph, scroll down!

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