Chapter 1.1

Is that equation linear?

• y = 3x – 4

Is that equation linear?

• y = 3x – 4

The equation is in the form y = mx + b,

where m = 3 and b = -4, so the equation

IS LINEAR.

Is that equation linear?

• 3y = x + 9

Is that equation linear?

• 3y = x + 9

Can the equation be arranged into theform y = mx + b?

Is that equation linear?

• 3y = x + 9

Can the equation be arranged into theform y = mx + b?

Yes

Is that equation linear?

• 3y = x + 9 Divide both sides by 3.y = 1/3 x + 3

The equation is in the form y = mx + b,where m = 1/3 and b = 3, so the

equationIS LINEAR.

Is that equation linear?

• 4y + 16 = 2x

Is that equation linear?

• 4y + 16 = 2x

Can the equation be arranged into theform y = mx + b?

Is that equation linear?

• 4y + 16 = 2x

Can the equation be arranged into theform y = mx + b?

Yes

Is that equation linear?

• 4y + 16 = 2x Subtract 16 from both sides of the equation.

4y = 2x – 16 Divide both sides of the equation by 4.

y = ½x – 4

The equation is in the form y = mx + b,where m = ½ and b = -4, so the equationIS LINEAR.

Graph: y = -2x + 3

Graph: y = -2x + 3

• m = -2/1• y-intercept = 3

• Start the graph at y-int (3).

• Use the slope (-2/1) and go down 2 and over 1.

Graph: y = 4x - 2

Graph: y = 4x - 2

• m = 4/1• y-intercept = -2

• Start the graph at y-int (-2).

• Use the slope (4/1) and go up 4 and over 1.

Graph: 6y + 36 = 6x

Graph: 6y + 36 = 6x

• Rearrange into y=mx+b.• Subtract 36 from both

sides 6y = 6x – 36.• Divide both sides by

6 y = x + 6.• m = 1/1• y-intercept = 6

• Start the graph at y-int (6).

• Use the slope (1/1) and go up 1 and over 1.

Does that table represent a linear equation? If so, provide

an additional ordered pair.

X Y

2 1

4 2

6 3

8 4

• Do the values of x increase at the same rate? Yes, they all increase by 2.

• Do the values of y increase at the same rate? Yes, they all increase by 1.

• If you answered “yes” to both of these questions, then the table represents a linear equation.

Does that table represent a linear equation? If so, provide

an additional ordered pair.

X Y

2 1

4 2

6 3

8 4

• Do the values of x increase at the same rate?

• Do the values of y increase at the same rate?

• If you answered “yes” to both of these questions, then the table represents a linear equation.

Does that table represent a linear equation? If so, provide

an additional ordered pair.

X Y

3 -1

6 -3

9 -5

11 -7

• Do the values of x increase at the same rate?

• Do the values of y increase at the same rate?

Does that table represent a linear equation? If so, provide

an additional ordered pair.

X Y

3 -1

6 -3

9 -5

11 -7

• Do the values of x increase at the same rate? No

• Do the values of y increase at the same rate? Yes, they all decrease by 2.

• We answered “No” to the first question, so it does not represent a linear equation.