You don't know how to go on because you don't know how to draw a linear equation without the use of a calculator? Fortunately, once you understand the procedure, drawing a graph of a linear equation is quite simple. All you need is to know a couple of things about the equation and you will be able to get to work. Let's get started.
Steps
Step 1. Write the linear equation in the form y = mx + b
It is called the y-intercept form and is probably the simplest form to use to graph linear equations. The values in the equation are not always whole numbers. Often you will see an equation similar to this: y = 1 / 4x + 5, where 1/4 is m and 5 is b.
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m is called the slope or, sometimes, the gradient. Slope is defined as an uphill run, or the change in y with respect to x.
Graph Linear Equations Step 1Bullet1 -
b is called the "y intercept". The y intercept is the point where the line meets the Y axis.
Graph Linear Equations Step 1Bullet2 -
x and y are the two variables. You can solve for a specific value of x, for example, if you have a point in y and you know the values of m and b. x, however, is never a single value: its value changes as it goes up or down on the line.
Graph Linear Equations Step 1Bullet3
Step 2. Identify the b number on the Y axis
b is always a rational number. Whatever the number b, find its equivalent on the Y axis and put the number on that point in the vertical axis.
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For example, let's consider the equation y = 1 / 4x + 5. Since the last number is b, we know that b is equal to 5. Go 5 points up on the Y axis and mark that point. This is where the straight line will cross the Y axis.
Graph Linear Equations Step 2Bullet1
Step 3. Make m into a fraction
Often the number in front of the x is already a fraction, so you don't have to transform it. If not, transform it by writing the value of m above 1.
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The first number (numerator) is the climb in the race. Indicates how much the line rises up, or vertically.
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The second number (denominator) is the race. Indicates how far the line goes to the side, or horizontally.
Graph Linear Equations Step 3Bullet2 - For instance:
- A slope of 4/1 rises by 4 for each side point.
- A slope of -2/1 drops by 2 for each side point.
- A slope of 1/5 goes up by 1 by 5 side points.
- For example, using the illustration above, you can see that for each point where the line goes up, it moves 4 to the right. This is because the slope of the line is 1/4. Extend the line on both sides, continuing to use the running climb concept to draw the line.
- Positive slopes go up, while negative slopes go down. A slope equal to -1/4, for example, will go down 1 point by 4 points to the right.
Step 4. Begin by extending the line from b using the slope
Start from the value of b: we know that the equation passes through this point. Stretch the line by taking the slope and using its values to get the points on the equation.
Step 5. Continue to lengthen the line, using a ruler and being careful to use the slope m as a guide
Stretch the line to infinity and you are done drawing your linear equation. It's easy, isn't it?
