5.3+++Connecting+the+Points+10-11

May 30, 2011 Madihah Haque Big Idea: Many real world situations can be modeled and predicted using mathematics. Essential Question:  How steep is that line? i. ii.
 * 5.3 Connecting Points **
 * For any two points, there is exactly one straight line that can be drawn through both points. In this problem, you will be given the coordinates of two points. Your task will be to find information about the line through these points-including its slope, its //y//-intercept, and the coordinates of other points that lie on the line. **
 * A. Plot the points on a coordinate grid, and draw the line that passes through them. **

For both i. and ii. The y values increase as the x values increase. i. 4-6/0-2=-2/-2= 1 ii. 3-6/2-4=-3/-2=3/2 Yes.  i. 4 ii. 1/2
 * <span style="color: black; font-family: Arial,sans-serif; font-size: 13pt;">B. Do the //y// values for points on the line increase, decrease, or stay the same as the //x// values increase? **
 * <span style="color: black; font-family: Arial,sans-serif; font-size: 13pt;">C. Find the slope of the line. **
 * <span style="color: black; font-family: Arial,sans-serif; font-size: 13pt;">D. Mark and label at least three other points on the line, and record the //x// and //y// values for the points in an organized table. Does the pattern in your table confirm the slope you found in part B? **
 * <span style="color: black; font-family: Arial,sans-serif; font-size: 13pt;">E. Use the graph or the table to find the //y­//-intercept of the line. **

<span style="color: black; font-family: Arial,sans-serif; font-size: 13pt;">If the slope if zero, the line is horizontal. If the first //x// values are negative, the line slants downwards (left to right). If the first //x// values is positive the line slants upwards, right to left. Slope: -3 y-intercept: 8
 * <span style="font-family: Arial,sans-serif; font-size: 13pt;">Problem 5.3 Follow-Up **
 * <span style="font-family: Arial,sans-serif; font-size: 13pt;">1. How can you sue the slope of a line to determine whether the line slants upward from left to right, slants downward from left to right, or is horizontal? **
 * <span style="font-family: Arial,sans-serif; font-size: 13pt;">2. The table below represents a linear relationship. Copy the table, and use the pattern to fill in the missing entries. Find the slope and the //y//-intercept of the graph of this relationship. Explain how you found your answers. **
 * < -7 ||< 0 ||< 1 ||
 * < -13 ||< 8 ||< 11 ||

= = <span style="color: black; font-family: Arial,sans-serif; font-size: 13pt;">2.4. = =
 * <span style="font-family: Arial,sans-serif; font-size: 13pt;">3. Confirm that the table below represents a linear relationship. What is the slope of the graph of this relationship? **