Graphing of Linear Equation in Two Variables
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1. To graph a linear equation in the form of y = mx + b, plot the y-intercept b on the y-axis, convert the slope m to a fraction if needed, then extend the line from the y-intercept using the rise over run of the slope. 2. The slope m represents the rise over the run and indicates the steepness and direction of the line, while the y-intercept b is the point where the line crosses the y-axis. 3. To graph the line, start at the y-intercept b, then continue extending the line using the fractional slope m by taking rises and runs to plot additional points and draw the line across the graph.
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2.2 linear equations and 2.3 Slope
The document discusses linear equations and slope. It covers plotting points on a coordinate plane, calculating slope using the rise over run formula, writing equations in slope-intercept form, finding the x- and y-intercepts, and graphing lines by making a table or using the slope and y-intercept. Methods are provided for determining the equation of a line given two points, the slope and one point, or from a graph.
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The document provides information and examples about coordinate planes and linear equations:
1) It reviews formulas for the standard form, slope-intercept form, and point-slope form of linear equations. Examples are given of writing equations from points and slopes using the point-slope form.
2) Classwork problems are assigned from section 2.11 and formulas/examples are provided to help with coordinate plane test preparation on writing linear equations from graphs.
3) Additional resources like Khan Academy and online guides are mentioned for further practice with coordinate plane and linear equation concepts.
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Graphing of Linear Equation in Two Variables
- 2. 1. Make sure the linearequation is in the formy = 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.
- 3. •m is called the "slope," or sometimes "gradient." Slope is defined as rise over run, or the change in y over the change in x.
- 4. •b is defined as the "y- intercept." The y- intercept is the point at which the line crosses the Y-axis.
- 5. •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.
- 6. 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.
- 7. •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.
- 8. 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 ofm over 1.
- 9. •The first number (numerator) is the rise in rise over run. It's how far the line travels up, or vertically.
- 10. •The second number (denominator) is the run in rise over run. It's how far the line travels to the side, or horizontally.
- 11. •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 points up for every 5 points over.
- 12. 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.
- 13. •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,
- 14. 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?
- 15. ••