1 Slope & Equations of a Line Section 1.1 Prepared by E. Gretchen Gascon

2 Slope - Definition Slope is defined as the change in y over the change in x, where the two points used are (x1, y1) and (x2, y2) This is an important formula to remember.

3 Example # 1(a) Find the slope of a line through two points This slope is said (1/11) The slope of a line parallel to this line would also have a slope of -(1/11) While the slope of a line perpendicular to this line would have a slope of +(11/1). Find the slope through (-7,6) and (4,5)

4 Example #1 (b) Find the slope of a line through two points This slope is 0, Meaning it has no slope or it is a flat line (horizontal) Find the slope through (5,-3) and (-2,-3)

5 Problem # 3 page 15 Find the slope of a line through two points This slope is said to be UNDEFINED, because division by 0 is not allowed This line is a vertical line and therefore the slope is undefined. Find the slope through (8,4) and (8,-7)

6 Slope Intercept form y = mx + b Where y and x represent all points on the line. m represents the slope of the line. and b represents the y value of the y-intercept of the line (x,y) This is an important formula to remember.

7 Problem # 7 page 15 find the slope of the line given an equation Given: 5x – 9y = 11 Re-write the equation in slope intercept form. y = mx + b m is the slope. The slope of this line is Subtract 5x, and then divide by -9 Because neg/neg = pos.

8 Problem # 13 page 15 Find the slope of a line parallel to a given line Given: 2y – 4x = 7 Re-write the equation in point slope form. y = mx + b m is the slope. The slope of this line is 2/1 The slope of a line || to the given line will have the SAME slope of the given line. The slope of the || line is 2 Note: The slope of a line perpendicular to the given line will have a slope = the negative reciprocal of the given line. The slope of a line perpendicular to 2y – 4x = 7 would be -1/2 Divide both terms on the right by 2 Any whole number (n) can be written as n/1

9 Point – Slope Equation - Definition Slope is m, and the point used is (x1, y1) If the problem gives two points, first find the slope, and then use either of the given points as the point for this equation.

10 Problem # 19 page 15 Find the equation of a line given two points Given: (4,2), (1,3), find the equation of the line. OR Find the slope first Then substitute either point into the slope intercept equation to find b. Note: If you already know the slope, skip step 1 Step 1 Step 2

11 Parallel and Perpendicular Lines Two lines are Parallel if and only if they have the same SLOPE Example: two lines both have a slope of 2/3, then they are parallel Two lines are Perpendicular if and only if the product of their slopes is -1 (one is the negative reciprocal of the other) Example: One line has a slope of ¾ and the other has a slope of -4/3, then they are perpendicular.

12 Comments Was there anything about this PowerPoint presentation that you would like explained further? Post comments or questions to the Main Forum or your Individual Forum. For more examples be sure to review the Practice Exercises posted in the course materials Forum of our class.