SLOPE LESSON 2 3 Algebra 2 Slope basically

SLOPE LESSON 2 -3 Algebra 2

Slope basically describes the steepness of a line If a line goes up from left to right, then the slope has to be positive Conversely, if a line goes down from left to right, then the slope has to be negative

Slope Formula In order to use that formula we need to know, or be able to find 2 points on the line

Procedure for Finding Slope (-3, 7) and (4, -6) Ø To find the slope given two points: Ø Ø Determine the values of x 1, x 2, y 1, and y 2 Substitute the value of each variable in the formula and solve Simplify the fraction as much as possible DO NOT write the fraction as a mixed number of a decimal

Examples of Finding Slope (4, -1. 5) & (3, 2. 5) (1/2, 2/3) & (5/6, 1/4)

Horizontal & Vertical Lines Horizontal lines have a slope of zero (when 0 is on top of a fraction) Vertical lines have no slope (when 0 is under the fraction bar) m=0 m = no slope

Your Turn: Find the slope of the line passing through each pair of points. Then Graph the line. 1. (-1, 4) and (1, -2) 2. (-2, -3) and (0, -5) 3. (5, -4) and (5, 6) 4. (2, -7) and (-3, -7)

Graphing a Line Given a Point and Slope (-4, -3) and m = 2/3 Ø To graph a line given a point on the line and the slope of the line: Ø Ø Ø Plot the given point on graph paper From that point, use your slope to find another point on the line Connect your points to draw the line

More Graphing… (2, -1) and m = 3 (-3, -4) and m = -3/2

More Graphing… (1, 4) and m = 0 (-2, -1) and m = no slope

Your Turn… Graph the line passing through the point (-3, -1) with m = -3

Standard Form and Slope If a line is in the form Ax + By = C, we can use the following formula to find the slope:

Examples of Finding Slope Given Standard Form 5 x – 4 y = 8 15 x + 3 y = 17

Parallel Lines & Slope Parallel lines have the same slope. Graph the line through (-1, 3) that is parallel to the line with equation x + 4 y = -4. Ø Ø Find the slope of the line with the given equation Plot the point you are given Use the slope you found to graph another point Draw a line through the points

Your Turn… Graph the line through (2, -1) that is parallel to the line with equation 2 x + 3 y = 6.

Perpendicular Lines & Slope The slopes of perpendicular lines are opposite reciprocals. What is a opposite reciprocal?

Perpendicular Lines & Slope Graph the line through (4, -2) that is perpendicular to the line with equation 3 x – 2 y = 6. Ø Ø Ø Find the slope of the line with the given equation Find the opposite reciprocal of this slope Plot the point you are given Use the opposite reciprocal slope you found to graph another point Draw a line through the points

Your Turn… Graph the line through (-1, 5) that is perpendicular to the line with equation 5 x – 3 y = 3.

Answer this question in your warm-up book. How does slope apply to the steepness of roads? Include the following in your answer: • A few sentences explaining the relationship between the grade of a road (the amount a road rises divided by the horizontal distance of the road) and the slope of a line • A graph of y = 0. 1 x which corresponds to a 10% grade (The scale on your x- and y-axes should be the same. )