Writing Linear Equations-STAAR Review

Writing Linear Equations

Using the y=mx+b form

Equation of a line: y=mx+b

• "m" is the rate or slope of the line

• "b" is the starting value

Multiple Choice

What is the slope in the equation $y=2x+3$ ?

• 2

• 3

• 5

• Cannot be Determined

Multiple Choice

What is the y-intercept in the equation $y=2x+3$ ?

• 2

• 3

• 5

• Cannot be Determined 

Multiple Choice

How would you write the equation with a slope of 7 and a y-intercept of -3?

• y = 7x + 3

• y = 7 - 3

• y = 7x - 3

• y = -7x + 3

Writing Equations from Word Problems

• Identify the starting value in the word problem. This is "b".

• Identify the rate. (Look for "per" or "each") This is "m".

• Plug in m and b into the equation y=mx+b.

Multiple Choice

Bob's Plumbing charges $25 per hour plus a service fee of $40 for coming out to your house. Which equation models this situation?

• y = 25x + 40

• y = 40x + 25

• y = 25x

• y = 25x - 40

Multiple Choice

Amelia has $100 in her savings account and plans on saving $20 per week. Write an equation to represent this situation.

• y = 100x

• y = 20x

• y = 20x + 100

• y = 100x + 20

Writing Equations from a Table

• First, identify b by finding where x=0 in the table. b= y value

• Pick two points from the table. Calculate m: $m=\frac{\Delta y}{\Delta x}=\frac{change\ in\ y\ values}{change\ in\ x\ values}$  

• Plug "b" and "m" into the equation.

Multiple Choice

Which equation matches the table?

• y = 3x + 9

• y = x + 9

• y = x + 3

• y = 12x - 3

Multiple Choice

What is the equation of the linear relationship shown in this table?

*Hint: Work backwards to find where x=0 for the y-intercept.

• y = -3x + 10

• y = -3x + 16

• y = 3x + 10

• y = 3x + 16

Writing Equations from a Graph

• Identify the y-intercept (where the line crosses the y-axis). This is "b".

• Pick two points that lie on the line.

• Put the points in a table or calculate  $\frac{rise}{run}$  to find "m".

• Plug in "b" and "m" to the equation y=mx+b.

Multiple Choice

Find the slope of this line.

• -5/7

• 7/5

• -7/5

• 5/7

Multiple Choice

Write the equation of the line.

• y = -1x - 3

• y = -3x - 1

• y = -1/3x - 1

• y = -3x - 3

Multiple Choice

What does the "b" stand for in y=mx+b?

• slope
• x-intercept
• y-intercept

Multiple Choice

What does the "m" stand for in y=mx+b?

• slope

• x-intercept

• y-intercept

Multiple Choice

Given the table, write the equation in the slope-intercept form (y = mx + b).

• y = 1/3x + 6

• y = 3x + 6

• y = 2x + 6

• y = 1/2x + 6

Multiple Choice

Connor has sold 15 cups of lemonade at his stand and will sell 5 more cups per hour. Write an equation to represent this situation.

• y = 10x + 5

• y = 20x

• y = 15x + 5

• y = 5x + 15

Multiple Choice

Which equation best represents the line on the graph?

• y= 1/2x
• y= -1/2x
• y = 2x
• y = -2x

Multiple Choice

Which equation matches the table?

• y = x 
• y = 5x
• y = x - 4
• y = x + 4

Multiple Choice

Sally plans to walk 12 miles every week. Write an equation to represent this situation.

• y = 12x

• y = 12x + 12

• y = 10x + 2

• y = 2x + 10

Multiple Choice

Which equation matches the table?

• y = x + 5

• y = 5x

• y = x - 5

• x = y - 5

Multiple Choice

Give the equation for the graph

• y = 5x - 3
• y = 4x + 2
• y =-2x + 5
• y = - 2x + 4

Multiple Choice

A man is climbing down from 100 feet high descending 30 feet per minute.

• y = 100 - 30x
• y = 100 + 30x
• y = 100x + 30
• y = 100x - 30

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation to represent this situation.

• y = 2x + 15

• x = 15y + 2

• y = 15x+ 2

Multiple Choice

What is the equation for the line that passes through the points (4,2) and (0,6)?

• y = x + 6
• y = -2x + 2
• y = -x - 6
• y = -x + 6

Multiple Choice

What is the equation for the line with a slope of 7 and passes through (0,1)?

• y = -7x + 1

• y = 7x + 1

• y = -1/7x - 1

• y = -1/7x + 1