1.3 Linear Equations in Two Variables

Objectives: Write a linear equation in two variables given sufficient information. Write an equation for a line that is parallel or perpendicular to a given line.

Standard: 2.8.11.A Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.

I. Point-Slope FormIf a line has a slope of m and contains the point

(x1, y1), then the point-slope form of its equation

is

y – y1 = m(x – x1).

Ex 1. Write an equation in point-slope form for the line that has a slope of ½ and contains the point (-8, 3). Then write the equation in slope-intercept form.

I. Point-Slope Form

Ex 2. Write an equation in point-slope form for the line that has a slope of 5 and passes through the point (-1, -3). Then write the equation in slope-intercept form.

II. Writing an equation in slope-intercept form

for a line containing two given points. Find the slope.

Substitute “m” & one of the two points you were given into y = mx + b to find “b.”

Write the equation in y = mx + b form with the values for “m” and the “b” that you calculated.

II. Write an equation in slope-intercept form for the line containing the two given points.

Ex 1. (4, -3) and (2,1)

II. Write an equation in slope-intercept form for the line containing the two given points.

Ex 2. (1, -3) and (3, -5)

III. Parallel and Perpendicular Lines

Parallel Lines – If two lines have the same slope, they are parallel. If two lines are parallel, they have the same slope. All vertical lines have an undefined slope and are parallel to one another. All horizontal lines have a slope of 0 and are parallel to one another.

y = 2x + 5 and y = 2x – 1

Perpendicular Lines – If a nonvertical line is perpendicular to another line, the slopes of the lines are opposite sign and reciprocal of one another. All vertical lines are perpendicular to all horizontal lines. All horizontal lines are perpendicular to all vertical lines.

y = 2x + 2 & y = -1/2x + 4

III. Parallel and Perpendicular Lines

(-2, 5), y = -2x + 4 Parallel Perpendicular

III. Parallel and Perpendicular Lines

(8, 5), y = -x + 2 Parallel Perpendicular

III. Parallel and Perpendicular Lines

1. (5, -3), y = 4x + 2 2. (-2, 3), y = -3x+2

3. (4, -3), 3x + 4y = 8 4. (-6, 2), y = -2/3 x - 3

For each of the following:

5. (1, -4), y = 3x – 2 6. (0, -5), y = x – 5

7. (3, -1), 12x + 4y = 8 8. (-2, 4), x – 6y = 15

Find a line that goes through the given point and is parallel to the given line.

Find a line that goes through the given point and is perpendicular to the given line.

Writing Activities: Parallel and Perpendicular Lines

1. Describe the relationship between the equations of 2 parallel lines. Include an example.

2. Describe the relationship between the equations of 2 perpendicular lines. Include an example.

Writing Activities: Parallel and Perpendicular Lines

3. Explain how to write an equation for the

line that contains the point (2, -3) and is

parallel to the graph of x – 2y = 2.

4. Explain how to write an equation for the

line that contains the point (2, -3) and is

perpendicular to the graph of x – 2y = 2.

Homework

Integrated Algebra II- Section 1.3 Level A even #’s

Honors Algebra II- Section 1.3 Level B