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Chapter 6 Test (Click on the "DISCUSSION" tab to ask or to answer questions) Things to know…. 1. Slope is a measure of the steepness of a line. a. The higher the slope the steeper the line b. Positive slopes slant up from left to right. c. Negative slopes slant down from left to right. d. Zeros slopes are horizontal. e. Undefined slopes are vertical. 2. To calculate slope… a. From a graph when counting is easy, RISE/RUN. Be careful to read the scale. b. From two points, (y2 - y1)/(x2 - x1). 3. To use slope to find other points… a. On a graph, count rise and run to mark new point. (Be careful that positive slopes go up and negative slopes go down. If there is no denominator shown, the run is 1.) b. When given a point, make the y-values increase by the numerator, make the x-values change by the denominator. 4. Equations for lines… a. When you know the slope and the y-intercept, y = mx + b {m = slope, b = y-intercept}. b. When you know a point and a slope, y – y1 = m(x – x1) {m = slope, (x1, y1) is a point}. i. When you have two points, calculate the slope then plug in either point. ii. Change to slope-intercept by distributing then adding y1 to both sides. c. Ax + By = C i. Graph by making a chart and plugging in zeros for x and y.  ii. Change to slope-intercept form by subtracting the x-term then dividing everything by B.  d. Vertical Lines take the form x = #. (x = 3 è (3, 0), (3, 1), (3, -4),…   e. Horizontal Lines take the form y = #. (y = 1 è (0, 1), (4, 1), (-5, 1),… 5. A set of points will form a line if the slope between them is constant (not changing). 6. IN REAL LIFE… a. Slopes appear as rates of change. i. Ex. Joe saved $150 each month ii. Ex. the temperature dropped by 2 ° F ever hour b. Points appear as … i. In 1988, the population was 23,000 people. è (1988, 23000) ii. After 2 months, there were 23 kids in the club. è (2, 23) c. Situations where 2 rates of change are given should be written in Ax + By = C form. i. Adults pay $12 and kids pay $8. The total price is $36. è 12x + 8y = 36 ii. John traveled at 25 miles per hour for the first part of the trip then he traveled at 40 miles per hour. The entire trip was 60 miles. 25x + 40y = 60. X = # of hours at 25 mph and y = # of hours at 40 mph.