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# The slope-intercept form of a line: y mx b - PowerPoint PPT Presentation

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?

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

• 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.

• 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