The Slope-Intercept Form of a Linear Equation

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Presentation transcript:

The Slope-Intercept Form of a Linear Equation Chapter 8 Section 8.4

Objective Students will use the slope-intercept form of a linear equation

Concept The points with coordinates (-2, -4), (-1, -2), (0, 0), (1, 2), and (2, 4) are on the graph of the linear equation y = 2x. What is the slope? What is the y-coordinate?

Concept For every real number m, the graph of the equation y = mx is the line that has slope m and passes through the origin

Concept The graphs of the linear equations y = 2x and y = 2x + 4 are shown at the right. The lines have the same slope, but they cross the y-axis at different points. The y-coordinate of a point where a graph crosses the y-axis is called the y-intercept of the graph.

Concept To determine the y-intercept of a line, replace x with 0 in the equation of the line y = 2x y = 2x + 4 y = 2(0) = 0 y = 2(0) + 4 y-intercept = 0 y-intercept = 4

Concept If you write y = 2x as y = 2x + 0, you can see that the constant term of each equation is the y-intercept of each graph: y = 2x + 0 y = 2x + 4

Concept For all real numbers m and b, the graph of the equation y = mx + b Is the line whose slope is m and whose y-intercept is b. This is called the slope-intercept form of an equation of a line

Find the slope and y-intercept of y = 3/5x + 2 Example Find the slope and y-intercept of y = 3/5x + 2

Find the slope and y-intercept of y = -2x – ½ Example Find the slope and y-intercept of y = -2x – ½

Concept When graphing using slope-intercept form y = mx + b

Use only the slope and y-intercept to graph y = -3/4x + 6 Example Use only the slope and y-intercept to graph y = -3/4x + 6

Use only the slope and y-intercept to graph 2x – 5y = 10 Example Use only the slope and y-intercept to graph 2x – 5y = 10

Concept Lines in the same plane that do not intersect are parallel. The following relationships exist between parallel lines and their slopes. 1. Different lines with the same slope are parallel 2. Parallel lines that are not vertical have the same slope

Show that 2x + y = 8 and 2x + y = 6 are parallel Example Show that 2x + y = 8 and 2x + y = 6 are parallel

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