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

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

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.

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.

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!!

In Other Words… xy 0 0

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

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”.

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

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.

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)

Find The Slope

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.

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