unit 5 ms. andrejko 5.1 notes x-intercept: where the line crosses the x-axis written as (x,0) ...

y

x

UNIT 5Ms. Andrejko

5.1 NOTES X-intercept: where the line crosses the

x-axis Written as (x,0)

Y-intercept: where the line crosses the y-axis Written as (0,y)

X-intercept

y-intercept

5.1 Notes To graph the line of an equation using

the intercepts: 1. Find the x-intercept of a given equation

by substituting a 0 for y, and solving for x

2. Find the y-intercept of a given equation by substituting 0 for x and then solving for y

(x , 0)

(0, y)

5.1 Examples 1. Find the x & y intercepts

5.1 Examples 2. Graph 3x+2y=6

3. Graph y= 2/3x +5

5.1 Examples 4. The ticket price for students (x) to

attend a school basketball game is $3 and adults (y) pay $5. The sports program took in $510. Equation:

X-intercept: Y-intercept:

X-intercept represents:

Bellwork1. 2. Graph: 3x -

4y = 12

X-intercept: 3. Graph: 5x + 2y = -10

Y-intercept:

5.2 NOTESSLOPE, X&Y INTERCEPTS1. Slope (m)2. To find the slope of a line:

1. Identify 2 points on the line with x&y values that are not fractions

2. Draw a slope triangle from the lower point to the higher point

3. Use of the triangle to write the slope. Rise is the height. Run is the length

riserun

5.2 NOTES4. Determine if the slope is negative or

positive by the direction of the line. * line going up from LR is

POSITIVE* line going down from LR is

NEGATIVE5. Reduce fraction if possible

positive negative

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zero

5.2 Examples

Slope:

X-int:

Y-int:

Slope:

X-int:

Y-int:

1. 2.

5.2 Examples

Slope:

X-int:

Y-int:

Slope:

X-int: (-3,0)

Y-int: (0,2)

3.

5.2 Examples

Slope: - ½

X-int:

Y-int: (0,2)

Bellworky

x

y

x

slope is: _______x-intercept is: ______y-intercept is: ______

slope is: _______x-intercept is: ______y-intercept is: ______y

x Slope: 2Y-intercept (0, -6)X-intercept ( , )

5.3 NOTES

Steps:1. Graph the y-intercept on the y-axis (1st

point)2. If the slope (m) is not a fraction, make it a

fraction by putting a 1 in the denominatorex: 2 = 2/1

y=mx+bY-interceptslope

5.3 NOTES3. From the point on the y-intercept, go up

the # in the numerator (rise), and go left or right the number in the denominator (run)

*If the slope is positive, go right* If the slope is negative, go left

4. Connect the two points. Make sure your lines have arrows!

5.3 Examples1. y=2x-1 2. y=-2x

3. y= ½ x+3 4. y= 2/3 x+5

5.3 Examples5. y= 0x+1 6 (a)

7 (b) 8 (c)

Bellwork

1. 2.

3. 4.

Y= ½ x +3 Y= -2x - 4

Equation: Equation:

5.4 NotesGoal: isolate the y-term on the right side

of the equal sign. Then, identify m and b & graph the line.

Steps:1. Move the x-term to the right side of the

= sign by adding its opposite2. If there’s a coefficient of “y” ( a # in

front of y), divide it by every term on both sides of the = sign to completely isolate the “y”

5.4 Examples Solve for y:a. x+y = 0 b. -2x -3y = 6

5.4 Examples Solve for y & GRAPH:a. 2x + ½ y = -2 b. -4x – 6y

= 12 y

x

y

x

Bellwork- Solve for y & graph

-x + y = 5 2x + y = -4

–x + y = -1 41x

y

x

y

x

y

5.5 Notes Connecting graphing a line using table of

values/intercepts/slopes

To graph the line of an equation using a table of values:

1. Choose 3 x-values, usually 0,1,2 or -1,0,1. Any 3 values will work, just make sure the points fit the graph.

2. Find the corresponding y-values by plugging each x-value into the equation where the “x” is, one at a time.

5.5 Notes3. Calculate the right side of the equation.

Whatever your answer is, put it in the y-value spot. This is a point on the line you will graph (x,y)

4. Graph the point5. Follow steps 1-4 for all 3 x-values6. Graph all 3 points & connect them to

form a straight line

5.5 Examples

5.5 Examplesd.Describe the difference in the lines of y = 2x and y

= -2x graphed above.

 e. What part of the equation, do you think, effects the

direction of the line? 

f. In “h” above, where does the line touch the y-axis?  g. Where do you think the line of y = x – 4 will

touch the y-axis?

5.5 Examples

When graphing an equation with a fraction, choose the negative and positive of the denominator (bottom) of the fraction and zero for the 3 values of “x”. This way none of the “y” values will end up fractions, which are much harder to graph.

BellworkY = x - 5 Y = ½ x +2 Y = 3x - 1

5.6 Notes Graphing Horizontal & Vertical Lines1. Equations w/ only ONE variable graph

either horizontal or vertical lines2. An equation with only a “y”, like y=1,

graphs a horizontal line3. An equation with only an “x”, like x=2,

graphs a vertical line• y=1, is the same as y=0x+1, so the

slope (m) is zero & y-intercept is 1

5.6 Notesx=1 cannot be written into y=mx+b

because it has no “y”. This equation has no slope & no y-intercept

4. Slope of horizontal line is 05. Slope of vertical line is undefined

5.6 Examples1. y=-2 2. x=3 3. 2y=4

Bellwork – Graph the lines:1. x=-5 2. 3x = 15

3. -4y=16