1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given...

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Transcript of 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given...

Page 1: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.
Page 2: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

1.2 Slopes and InterceptsObjectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane.

Standards: 2.8.11.K Apply an appropriate technique to graph a linear function. 2.8.11.L Write the equation of a line when given the graph of the line.

Page 3: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

I. Write the equation in slope-intercept form for the line that has the indicated slope, m, and y-intercept, b.

m = 3, b = -2 y = 3x - 2

m = ½, b = ¾ y = 1/2x + 3/4

m = 0, b = 5 y = 5

m = -2, b = 0 y = -2x

Page 4: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

II. Identify the slope, m, and y-intercept, b, for each line.

Then graph. Positive slope goes up to the right & negative

slope goes down to the right.

y = x + 3 *m = _______b = _______

x + y = 6 *m = _______b = _______

Page 5: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

II. Identify the slope, m, and y-intercept, b, for each line. Then graph.

3x + 6y = 18 *

m = ________

b = ________

Page 6: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

III. Find the slope of a line if you know the coordinates of two points on the line.

In a graph, the slope of a line is the change in vertical units divided by the corresponding change in the horizontal units.

m = Change in y = Rise = y2 – y1

Change in x Run x2 – x1

(0, 4) and (3, 1)

Page 7: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

m = Change in y = Rise = y2 – y1

Change in x Run x2 – x1

(1, -3) and (3, -5)

(3, -2) and (4, 5)

(-10, -4) and (-3, -3)

Page 8: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

IV. Find the x and y intercepts.

The x intercept of a graph is the x-coordinate of the point where the graph crosses the x-axis. In order to find the x intercept (x, 0), substitute zero for y in an equation for the line and solve for x.

The y intercept of a graph is the y-coordinate of the point where the graph crosses the y-axis. In order to find the y intercept (0, y), substitute zero for x in an equation for the line and solve for y.

Page 9: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

IV. Find the x and y intercepts.

4x + y = -4

x-intercept

y-intercept

x + ½ y = -2

x-intercept

y-intercept

Page 10: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

IV. Find the x and y intercepts.

1. x + 3y = 12 2. -3x + y = -9

3. x – y = -1 4. 5x – 8y = 16

5. 7x + 3y = 2 6. -x + 8y = -6

Page 11: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

V. Vertical Lines vs. Horizontal Lines

A horizontal line is a line that has a slope of zero.y = # is a horizontal line.

A vertical line is a line that has an undefined slope.x = # is a vertical line.

x = -2 Vertical Line Undefined Slope

y = 2 Horizontal Line Zero Slope

y = 9 Horizontal Line Zero Slope

Page 12: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

VI. Write an equation in slope intercept form for each line.

Ex 1. A line passing through (2, 4) with a slope of ½.

Ex 2. A line with a slope of zero passing through (-2, -6).

Zero slope means it’s a horizontal line so y = #

Page 13: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

VI. Write an equation in slope intercept form for each line.

Ex 3. A line passing through (0, -1) and (2,2).

Page 14: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

Writing Activities: Slopes and Intercepts

1a). In your own words, define the slope of

a line.

1b). Give an example of three lines with the

same slope.

Page 15: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

Writing Activities: Slopes and Intercepts

2a). In your own words, define the y-intercept of a line.

2b). Give an example of three lines with the

same y-intercept.

Page 16: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

Writing Activities: Slopes and Intercepts

3). What are the characteristics of a line that

has the equation y = mx?

4). What does the slope of a line indicate

about the line? Include some examples.

5). Explain the difference between a line

with a slope of 0 and a line with no

slope.

Page 17: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.
Page 18: 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply.

Homework

Integrated Algebra II- Section 1.2 Level A

Honors Algebra II- Section 1.2 Level B