Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
3. PLOTTING POINTS Remember when plotting points you always start at the origin. Next you go left (if x-coordinate is negative) or right (if x-coordinate is positive. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) Plot these 4 points A (3, -4), B (5, 6), C (-4, 5) and D (-7, -5) A B C D
4. SLOPE Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run. Slope triangle between two points. Notice that the slope triangle can be drawn two different ways. Rise is -10 because we went down Run is -6 because we went to the left Rise is 10 because we went up Run is 6 because we went to the right Another way to find slope
5. FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line. EXAMPLE
6. Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. Then use the formula
7. X AND Y INTERCEPTS The x-intercept is the x-coordinate of a point where the graph crosses the x-axis. The y-intercept is the y-coordinate of a point where the graph crosses the y-axis. The x-intercept would be 4 and is located at the point (4, 0). The y-intercept is 3 and is located at the point (0, 3).
8. SLOPE-INTERCEPT FORM OF A LINE The slope intercept form of a line is y = mx + b, where “m” represents the slope of the line and “b” represents the y-intercept. When an equation is in slope-intercept form the “y” is always on one side by itself. It can not be more than one y either. If a line is not in slope-intercept form, then we must solve for “y” to get it there. Examples
9. Put y – x = 10 into slope-intercept form Add x to both sides and would get y = x + 10 Put 2y – 8 = 6x into slope-intercept form. Add 8 to both sides then divide by 2 and would get y = 3x + 4 Put y + 4 = 2x into slope-intercept form. Subtract 4 from both sides and would get y = 2x – 4. IN SLOPE-INTERCEPT NOT IN SLOPE-INTERCEPT y = 3x – 5 y – x = 10 y = -2x + 10 2y – 8 = 6x y = -.5x – 2 y + 4 = 2x
10. GRAPHING LINES BY MAKING A TABLE OR USING THE SLOPE-INTERCEPT FORM I could refer to the table method by input-output table or x-y table. For now I want you to include three values in your table. A negative number, zero, and a positive number. Graph y = 3x + 2 By making a table it gives me three points, in this case (-2, -4) (0, 2) and (1, 5) to plot and draw the line. See the graph. INPUT (X) OUTPUT (Y) -2 -4 0 2 1 5
11. Plot (-2, -4), (0, 2) and (1, 5) Then draw the line. Make sure your line covers the graph and has arrows on both ends. Be sure to use a ruler. Slope-intercept graphing
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15. Exercises 3A 1,2,3 3B 1,2 4a c f 3C 1 a c f k l, 2 a d e g, 3 a c f 3D 1, 2 3E 2 3F 1,3,4
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