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Slope and Y-Intercept

Slope and Y-Intercept. Presented by Rebecca Soltis.

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Slope and Y-Intercept

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  1. Slope and Y-Intercept Presented by Rebecca Soltis

  2. This is determined by two number lines that cross. The horizontal line or the “sideways line” is called the x-axis and the vertical line or the “up and down line” is called the y-axis. These two axis cross to form what is called a coordinate plane. An example of a coordinate plane is shown below. The Coordinate Plane • _________________________________________

  3. ________________________________________ A point on a coordinate plane is designated (x, y). X represents the number of units on the horizontal x-axis and y represents the number of units on the vertical y-axis, from the point of origin designated (0, 0). For example, the point (2, 5) would be over 2 units to right and 5 units up, from the point of origin. This example is shown on the coordinate plane below. Points on the Coordinate Plane

  4. ________________________________________ A linear equation can be graphed on a coordinate plane. The standard form for a linear equations is y=mx+b (slope-intercept form), where m is the slope of the line, b is the y-intercept and x and y are points on the coordinate plane. You will learn about slope and y-intercept next. For now, concentrate on recognizing a linear equation and knowing the meaning of the variables in the equation. The Linear Line Graph example of slope-intercept form of a linear equation.

  5. ________________________________________ Slope can be either positive or negative. You can tell whether the slope of a line is positive or negative by looking at slope value in the equation or looking at which direction the graph of the line points. When a line has a positive slope, the right side of the graph will be higher. When a line has a negative slope, the right side of the graph will be lower than the left. I have provided an exampled of a graphs with both positive and negative slope. Slope Positive Slope Negative Slope

  6. __________________________________________ If you do not have the equation of a line, you can still find the slope. The slope of the line can be calculated using two points from the graph, (X1, Y1) and (X2, Y2), as follows: Y2 - Y1 __________________ X2 - X1 Example: (2, 4) and (4, 8) are two points of a line. To find the slope of the line: 8 – 4 _________________ 4 – 2 equals 2. The slope of the line is 2. Slope Continued

  7. ___________________________________________ Another way to find the of slope of a linear line is to compute the rise over the run. To do this, you take two different points on the line. From each point, draw a line until the two lines intersect (look at the picture below). Then, count the number of horizontal units (called the run) and the number of vertical units (called the rise). Compute the rise over the run to get the slope of the line. Slope Continued Example: Rise/Run = 2/3 Looking at the line, we know it has a negative slope so the slope of the line would be – 2/3. Picture courtesy of Math for Morons Like Us

  8. __________________________________________ In the slope-intercept form (y=mx+b) the variable b represents where the graph of the equation crosses (or intercepts) the y-axis. When a graph intercepts the y-axis at 0, b=0. Therefore, the equation will have the form y=mx. Below are two examples. The graph on the right is an example of a line that intercepts the y-axis at 0. Y-Intercept

  9. __________________________________________ Now that you know how to find the slope and y-intercept of a line, you can find the equation by looking at the graph of the line. First, begin by choosing two different points on the line. Use these points to compute the slope (the rise over the run). Second, look where the line intersects the y-axis to find the intercept. Third, use the two values for the slope-intercept form to determine the equation of the line. Finding the Equation Example: find the equation of the line from the graph on the right. First: using the two points (1, 5) and (2, 8), draw imaginary lines to compute the rise over run. From that computation, you should determine that the slope of the line is 3. Second: the line intersects the y-axis at 2 so the y-intercept is 2. Third: use the values for the slope intercept form. m=3 and b=2 so the equation for the line is y=3x+2.

  10. __________________________________________ • Worksheet – solve these problems to become a pro!! • Worksheet Answers – check the answers to the worksheet problems. • Student Resources – this page has great information about slope and y-intercept. I have even listed a fun game! Back to Main Page Practice

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