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

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

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### 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 calculator:

- 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? y-intercept and slope.

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: written in standard form:

- 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: written in standard form:

- 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

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