Writing Linear Equations The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step. We call this ratio the slope of the line. Slope is also known as the rate of change. 60 Speed (mi/h) 0 0 0 0 0 0 0 0 x Time (s) P a g e
Positive Slope from a Table Negative Slope from a Table P a g e
Find the slope of each line that passes through each pair of points. A(, ) and B(-, 0). A (, -) and B (, ). C (-, ) and D (, ). J (-, 8), K (-, ). P (,-7), Q (-,-7) P a g e
A scout ant discovers that sugar has been spilled on Karen's kitchen countertop. The ant marks a straight line trail from the sugar back to the hole in the wall where ants can crawl directl onto the countertop. The sugar is 8 feet from the hole in the wall. The graph and table below describe the movement of the Ant along a path that is a straight line. t d(t) 0 0 0 6 8 8 6 8 8 0 0. Find the average rate of change of the Ant during the interval(s) it is heading back toward the wall.. At what intervals is the slope negative. What is the slope on those intervals.. At what intervals is the slope positive. What is the slope on those intervals.. At what intervals is the slope constant. What is the slope on those intervals. 6. What is the average speed of the ant on the interval 0 t 6 7. What is the average speed of the ant on the interval 8 t 6 8. What is the average speed of the ant on the interval t 0 P a g e
A second ant slips through the wall onto the kitchen counter at time t = seconds and the for 8 seconds follows the trail directl to the sugar(which is 8 feet awa). The ant collects sugar for seconds and crawls directl back to the wall entrance. The return from the sugar to the wall takes seconds.. Draw a graph to illustrate the stor and then complete the table. t 0 d(t) 0 8. Find the average rate of change of the Ant during the interval(s) it is heading toward the sugar.. At what intervals is the slope negative. What is the slope on those intervals.. At what intervals is the slope positive. What is the slope on those intervals.. At what intervals is the slope constant. What is the slope on those intervals. P a g e
Graph the following situation: A swimmer climbs a ladder for seconds to a waterslide that is 6 feet high. She sits for seconds at the top of the slide, and then slides 9 feet down the slide into the water in seconds. She staed stead at the same position underwater for seconds before rising to the surface of the water in second. She remained in the pool for more seconds. a. Determine the average rate of change for the swimmer going up the ladder. b. During what time interval is the slope negative? c. At what time is the slope zero? d. Determine when the slope is positive. 6 P a g e
The Ant and the Sugar A scout ant discovers that sugar has been spilled on Karen's kitchen countertop. The ant marks a straight line trail from the sugar back to the hole in the wall where ants can crawl directl onto the countertop. The sugar is 8 feet from the hole in the wall. The graph and table below describe the movement of the Ant along a path that is a straight line.. How far did the ant travel in 0 seconds?. Does the graph represent the path that the ant took during the first 0 seconds?. What is the Ant's average speed for the time interval 0 t 0. Include units.. What is the Ant's average speed for the time interval 0 t 0. Include units.. Is the Ant's average speed increasing, decreasing, or constant. 7 P a g e
A scout ant discovers that sugar has been spilled on Karen's kitchen countertop. The ant marks a straight line trail from the sugar back to the hole in the wall where ants can crawl directl onto the countertop. The sugar is 8 feet from the hole in the wall. The graph and table below describe the movement of the Ant along a path that is a straight line. t d(t) 0 0 6 0 8 8 6 8 0. What is the Ant's average speed for the time interval 0 t 8. Include units.. What is the Ant's average speed for the time interval 0 t. Include units.. What is the Ant's average speed for the time interval 0 t 0. Include units.. What is the Ant's average speed for the time interval 6 t 8. Include units.. What is the Ant's average speed for the time interval 6 t. Include units. 6. What is the Ant's average speed for the time interval t 8. Include units. 7. According to the graph when was the Ant moving the fastest? 8. According to the graph when was the Ant moving the slowest? 8 P a g e
Use the equations below to find the average rate of change on the given intervals. = x + a) x = 0 to x = b) x = to x = c) x = - to x = -. x a) x = 0 to x = b) x = to x = c) x = - to x = - 9 P a g e
Finding the -intercept of a line The -intercept is the coordinate of the point where a line crosses the -axis, it s also the initial value when x = 0. Determining the -intercept of a table a. b. c. 0 P a g e
Example : = mx + b Slope-Intercept Form of Linear Equations: (m stands for slope and b stands for -intercept). = x + 7 slope -intercept. = x 8 slope -intercept. = 6 7x slope -intercept. = 0x slope -intercept. = slope -intercept 6. Given slope of 9 and the -intercept is. 7. Given slope of 0 and the -intercept is. 8. Given m and 6 b. 9. Given m and b. 0. Given m and the -intercept is (0, ).. Given slope of 0. and b 0. 6 P a g e
Graph the linear equations: (Hint: identif the slope and -intercept). Graph: x.. Graph: x. x x. Graph: x. x x x P a g e
Graphing Equations b Making Tables:.. P a g e
Writing Linear Equations Use the graph to determine the linear equation..... Use the table to determine the linear equation in slope-intercept form.. x - 6-8 - 0 8 x - - 7 - - 0 P a g e
Writing Equations based on a point and slope: Use the information provided to determine the linear equation in slope-intercept form.. Given m and the point (-, ). x. Given m and the point (-, 0). x. Given m and the point (-, -). x P a g e
Writing Equations based on points:. Graph a line that goes through the following points,,,, and write the equation. 8 7 6 8 7 6 6 7 8 x 6 7 8. Graph a line that goes through the following points,,,, equation. 8 7 6 and write the 8 7 6 6 7 8 x 6 7 8 6 P a g e
Finding Equations in point slope and slope intercept form Given Points: Use the information below to write a linear equation. A. (, ) & (, ) B. (6, -) & (-, ) Use the information below to write a linear equation. A. (, 7) & (, -) B. (6, -) & (-, -) 7 P a g e
Graph each pair of lines on the same coordinate plane. Make sure ou list the slope of each line.. x and x. x and x. x and x x x x. x and x. Graph x and x. x and x x x x 8 P a g e
Write in point-slope form the equation of the line that is parallel to the given line and passes through the given point. Your final answer should be in slope-intercept form.. = x +, (-, -). = -x +, (, ). x 6, (, ) m = m = m = point point point point-slope: point-slope: point-slope: Write in point-slope form the equation of the line that is perpendicular to the given line and passes through the given point. Your final answer should be in slope-intercept form.. = x +, (-, -). = -x +, (, ). x 6, (, ) m = m = m = point point point point-slope: point-slope: point-slope: 9 P a g e
Write in point-slope form the equation of the line that is parallel to the given line and passes through the given point. Your final answer should be in slope-intercept form.. x + =, (-, -). - x+ = 6, (, ). x - = 0, (, ) m = m = m = point point point point-slope: point-slope: point-slope: Write in point-slope form the equation of the line that is perpendicular to the given line and passes through the given point. Your final answer should be in slope-intercept form.. x + =, (-, -). - x+ = 6, (, ). x - = 0, (, ) m = m = m = point point point point-slope: point-slope: point-slope: 0 P a g e