Graphing Linear Equations

Finding Slope of a Line

100

Identify the slope of the following equation. y = mx + b

the variable m

200

Identify the slope of the following equation. y = 2x + 3

slope is 2

300

Name three ways to describe slope.

Possible answers: 

rate of change 

rise over run 

y - y/x - x 

slope = m in y = mx + b

400

Find the slope of the line that includes the following points. (4, -5) (-4, 5)

-10/8 which simplifies to -5/4

500

Find the slope of the line that includes the following points. (-12, -9) (-3, -3)

-6/-9 = 6/9 = 2/3

Graphing Linear Equations

100

What form do we use to graph a linear equation?

the slope-intercept form y = mx + b

200

When graphing linear equations, where do we begin?

We begin at the y-intercept.

300

Graph the following equation. Include at least 3 points. y = 1/3x + 4

Graph should start with the point at (0, 4) Movement should be 1 up and 3 to the right continuing to another point. Movement could also be 1 down and 3 to the left.

400

Graph the following equation. Include at least three points. y = -2

Graph should begin with a point on the y-axis at -2. A horizontal line should be drawn through -2 extending on both sides of the y-axis.

500

Make a table of values with at least 4 ordered pairs for the following equation. y = 1/2x -5 Then plot the ordered pairs. Draw a line through the points.

Table should list four numbers chosen for x and then solved by multiplying by 1/2 and subtracting 5. If x is 2 then If x is 4 then 1/2(2) = 1 - 5 1/2(4) = 2 - 5 then y = -4 then y = -3

Slope-Intercept Form

100

What is slope intercept form?

y = mx + b

200

In the following linear equation, what is the y-intercept? y = -3/4x

0

300

Rewrite this equation in slope-intercept form. x + y = -12

y = -x - 12

400

Rewrite the following equation in slope-intercept form. 3x + 6y = -18

y = -1/2x - 3

500

Rewrite the following equation in slope-intercept form. 3.5x - 7y = -21

-7y = -3.5x + 21 y = 0.5x - 3 or y = 1/2x - 3

RANDOM ?'s

100

Evaluate:

-2 - 5

-7

200

Solve for x:

3x - 2 = -14

x = -4

300

What is the slope of this equation?

 x = 5

Undefined Slope

400

Graph the following equation. 8x + 4y = 16

Should be rewritten as y = -2x + 4 and then graphed.

500

Is x = 2 a solution to the equation 2(x - 5) + 3 = 13  ?

No it is not a solution.

Writing Equations

100

What form of equations do we use for lines?

y = mx + b   or slope intercept form. 

200

Write an equation for a vertical line through the point (-3, 3)

x = -3

300

Write an equation for a line with the following slope and points.

 m = 2/3   and (0, -2),  (3, 0)

y = 2/3x - 2

400

Write an equation for a line with the following two points. Find the slope and y intercept. (15, -10) (5, 10)

slope = -2 y intercept = 20

y = -2x + 20

500

The amount y(in dollars) of money you have left after playing x games at a carnival is y = -0.75x + 10. How much money do you have after playing eight games? Graph the equation and show your explanation.

y = -0.75(8) + 10 y = -6 + 10 y = 4 $4 dollars left after playing 8 games. Graph should begin at (0, 10) on the y-axis and move down three and four to the right.

Point Slope Form

100

How do you write something in Point Slope Form?

y-y1=m(x-x1)

200

Write the  equation in point slope form of a line that passes through the given point and has the given slope

(1,2) m=-4

y-2=-4(x-1)

300

Write the equation in point slope form: 

(-1,-4); =-2

y+4=-2(x+1) 

or 

y-(-4)=-2(x-(-1))

400

Write the linear equation of a point that goes through (4,8) with a slope of m=3/4

y=3/4x+5

500

Write the Linear Equation (y=mx+b) based on the 2 points: (2,4) and (3,6)

M=2

y-4=2(x-2)

y=2x

Graphing Linear Equations in Standard Form

100

What is the standard Form of a linear equation? 

Ax+By=C

200

Find the X intercept of the following Equation:

x+3y=-3

X=-3

300

Find the Y intercept of the following equation:

2x-y=8

y=8

400

Find the X and Y intercepts:

15x-12y=60

x= (4,0) or 4

y= (0,5) or 5

500

You have $6 to spend on apples and bananas. The equation 1.5x + .6y = 6 represents this situation, where x is the number of pounds of apples and y in the number of pounds of bananas. Find the x and y intercepts 

x=4 or (4,0)

y=10 or (0,10)