3.5: lines in the coordinate plane objective: to graph and write equations of lines

3.5: Lines in the Coordinate Plane

Objective: To graph and write equations of lines

Slope

Type 1: Brainstorm everything you know about slope!

Slope is…… = = vertical change = change in y horizontal change change in x

SLOPE IS……………..RATE OF CHANGE!!!!

runrise

xy

To find the slope of a line passing through 2 points:

The 2 points it passes through are and

slope =

• Positive slope rises to the right• Negative slope falls to the right• Remember, ..all are a negative slope

11, yx 22 , yx

12

12

xxyym

41

41

41

Find the slope of the line that passes through the two given points.

1. ( 5, 1); (8, 3)

2. (1, -6); (9, -8)

3. (-5, -9); (-1, -1)

To find the slope of a line from a graph:

1. Find two points on the line and calculate the slope between them

2. OR….find a starting point on the line. Count how many units you go up or down, and then how many you go left or right until you hit the line again.

Calculate the slope of the line.

Lines in the Coordinate Plane

SLOPE INTERCEPT FORM: y = mx + b

m = slopeb= y intercept (where the line crosses the y-axis)

To graph in Slope-Intercept form:1. Graph your y-intercept, (0, b)2. Use the slope, m, to graph other points ( slope = vertical change

horizontal change)

Graph the following.

221

xy

Graph the following:

1.

2.

221

xy

221

xy

xy 4

Re-writing in Slope Intercept form

• Isolate y using algebra. Should look like y=mx+b

What is the slope and y-intercept of the following:1. -2x +3y = 9

2. x+ 6y = 4

3. -4x + y = -7

Now graph these lines.

Horizontal and Vertical Lines

Vertical lines: x= a, slope is undefined Horizontal line: y= b, slope is 0

Write the equation of the horizontal and vertical line that passes through the point (-2, 3).

The following is a graph that represents distance over time. Talk about what could be happening in this graph.

STANDARD FORM: Ax + By = C(Just a different form of a line. Can use algebra to move back and forth between

forms.)

To graph in Standard form: 1. Find x and y intercepts:

At y intercept, x is ALWAYS 0 At x intercept, y is ALWAYS 0

2. Graph both points. Draw a line through the points.

Graph 6x +3y = 12.

1. Find y intercept. (substitute 0 in for x)

2. Find x intercept. (substitute 0 in for y)

3. Graph both points.

GRAPH: - 2x + 4y = -8

Point Slope Form: 11 xxmyy

• Just another form of a line• Use to write an equation when given a point, ,

and a slope, m

Write the point slope equation of a line through the point (-1, 4) with a slope of 3.

),( 11 yx

You can re-write equations in different forms by using algebra.

1. Write the slope intercept equation of a line that passes through the point (2, -4) with a slope of -1 .

2. Write the slope intercept form equation of a line that passes through the point (-3, -1) with a slope of 4.

Write the slope intercept equation of the line that passes through the points (-2, 3) and (1, -1).

Need to find the slope first:

Use this slope and either point to write the equation.

Writing an equation from a graph.

1. Pick a point on the line. (If the y-intercept is easy to find, use that as a point.)

2. Find the slope from the graph. 3. Use the point and the slope to write equation.

Write the equation of the line shown in the graph.

Write the equation of the line shown in the graph.

WRAP UP: A 12-ounce tube of sun screen costs $3.50. An 18-ounce tube costs $5.00.

1. Write two ordered pairs that satisfy the relationship.

2. Write the linear equation. 3. Use the equation to find the cost of a 24-ounce

tube.4. Explain why the cost for 24 ounces is not twice as

much as the cost of 12 ounces.