The slope-intercept form of a line: y = mx + b

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Presentation transcript:

The slope-intercept form of a line: y = mx + b

Graph the following family of lines using the graphing calculator: y = 3x + 2 y = 5x + 2 y = -4 x + 2 y = 1/2 x + 2 All of these equations are written in y = mx+b form. What does m represent in each equation? Check your hypothesis by using the table feature of the calculator.

Graph the following family of lines using the graphing calculator: y = 3x + 2 y = 3x - 4 y = 3x y = 3 x + 8 All of these equations are written in y = mx+b form. What does b represent in each equation? Check your hypothesis by using the table feature of the calculator.

Given y = mx + b m represents the slope of the line b represents the y-intercept -- the point where the line intercepts or crosses the y-axis.

Graphing lines in the form y = mx + b is very easy since you know one point, the y-intercept, and the slope. Graph each of the following: y = 2x + 5 y = - x – 3 y = 4x y = - 2

Finding the equations of lines is very easy if you know the y-intercept and slope. Find the equation of the line: that passes through the origin with slope – 2. with y–intercept of 4 and slope 2/3. that is horizontal and passes through the point ( 2, 5)

What if the equation is not given in y = mx + b form? Graph the equation whose standard form is 3x + 2y = 6. Strategy 1: Rewrite the equation in y = mx + b form. Strategy 2: Find the x-intercept and the y-intercept.

To find the x-intercept and the y-intercept of a line written in standard form: Let x = 0 to find the y-intercept. Let y = 0 to find the x-intercept. Example: Find the x-intercept and the y-intercept of the line 3x – 5y = 15. Then graph the line.

Graphing equations in different forms: Point-slope form: y – y1 = m(x – x1) Use a point (x1, y1 ) and the slope, m. Standard form Ax + By = C Rewrite in y = mx + b form OR Find the x-intercept and the y-intercept OR Make a table of solutions. Slope-intercept form y = mx + b Use the y-intercept and the slope.

Assignment: 6.4 #19-45 odds Due Wednesday 1/14/04 6.5 #13-25 all. Use graph paper. Write the equation next to each graph. Due Thursday 1/15/05