1. MTH 091 Section 13.3 Graphing with x- and y-intercepts Section 13.4 Slope

2. So far…. In Section 13.1 we reviewed the Coordinate Plane and learned what a linear equation is. Then, we learned how to create a table of values. A table of values produces ordered pairs that can used to graph a linear equation. The graph of every linear equation is a straight line. The line may slant upwards or downwards, or be horizontal or vertical.

3. In These Sections Section 13.3 introduces intercepts and how they can be used to graph a line. Section 13.4 introduces the idea of slope.

4. x-intercepts and y-intercepts The x-intercept of a line is the point on the graph where the line crosses the x-axis. To find an x-intercept, set y = 0 and solve for x. Your ordered pair will be (___, 0). The y-intercept of a line is the point on the graph where the line crosses the y-axis. To find a y-intercept, set x = 0 and solve for y. Your ordered pair will be (0, ___). Do NOT find the x-intercept and y-intercept and make an ordered pair out of them!!

5. In Other Words… xy 0 0

6. Examples Find the x-intercept and y-intercept and graph: x – y = -4 y = 2x y = 2x + 10 2x + 3y = 6

7. What Is Slope? The slope of a line is its steepness, or slant, as viewed from left to right. If a line slants upward from left to right, it is said to have a positive slope. If a line slants downward from left to right, it is said to have a negative slope. A horizontal line has zero slope. There is no such thing as “no slope”. A vertical line has undefined slope. There is no such thing as “no slope”.

8. Examples Given the following slopes, determine if the line is upward sloping, downward sloping, horizontal or vertical: 1.m = -5/6 2.m = 3 3.m = 8/0 4.m = 0/7 5.m is undefined

9. Finding Slope Given Two Points Given two points and, the slope m of the line through the two point is given by If 0 is on the top, your slope is zero and the line is horizontal. If 0 is on the bottom, your slope is undefined and the line is vertical. Be sure to reduce to lowest terms.

10. Examples Find the slope of the line through: (-1, 5) and (6, -2) (1, 4) and (5, 3) (-8, 3) and (-2, 3) (-2, -3) and (-2, 5)

11. Find The Slope

12. Finding Slope Given An Equation A linear equation in slope-intercept form is given by y = mx + b, where m is the slope of the line and (0, b) is the y-intercept. If your equation is in standard form, you can convert it to slope-intercept form by isolating the variable y. If your equation is in the form x = h, the line is vertical and the slope is undefined. If your equation is in the form y = k, the line is horizontal and the slope is zero.

13. Examples Find the slope of the line: y = -2x + 6 -5x + y = 10 3x – 5y = 1 y = -3 x = 5