Forms of Linear Equations

Slope-Intercept

100

Find the intercept of the equation, y = ^-5⁄₃x - 4

(as a coordinate)

(0,-4)

200

Which of the following points are on the line represented by the equation 

y = 4/3x -2?

(2, 3)      (-2,0)      (-3, -6)

(-3,-6)

300

Write the equation 

5x - 4y = 20 

in slope-intercept form.

y = ⁵⁄₄x - 5

400

DOUBLE JEOPARDY! THIS QUESTION IS WORTH DOUBLE THE AMOUNT OF POINTS!

What is the equation of a line in slope-intercept form with a slope of -1 and f(0)=0

y=-x

500

A Caribbean nation produced 0.7 million tons of cane sugar. Annual production was projected to decrease by 0.05 million tons each year. Write an equation in slope intercept form to model the situation.

y = 0.7 - 0.05x

OR

y = -0.05X + 0.7

Point Slope Form

100

Write an equation in slope-point form that passes through (2, 0) and has a slope of - 5

y - 2 = -5(x)

*this is the same as y - 2 = -5(x - 0)

200

Write an equation in slope-point form that passes through the point (-2,3) and has a slope of 2/3

y - 3 = 2/3 (x + 2)

300

A line has a point at (9,6) and has a slope of 3. What is the equation of the line in Slope-Intercept form? (hint: you will need to use slope-point form first)

Y = 3X - 21

400

The line 

y − 4 =− 3(x + 8) 

goes through the point (k, 7). 

Determine the value of k.

k = -9

500

The line 

y + 6 = 4/3 (x + C) 

has a y-intercept of 2. Determine the value of c.

C = 6

General Form

100

True or False: The following equation is in General Form:

0 = -3X + 2Y - 8

FALSE

200

Convert the following equation into General Form:

y = 1/2X - 4

X - 2Y - 8 = 0

300

Which of the following points is NOT on the line represented by the equation 

3X - 5Y - 4 = 0?

(8, 4)   (0, -0.8)   (-2,2)   (-3,1)

(-2,2)

400

Convert the following equation into general form:

Y + 9 = -4/3(X - 3)

4X +3Y + 15 = 0

500

The line 

3x + 4y - C = 0 

contains the point (-1, -4). What is the value of C?

C = -19

Parallel & Perpendicular Lines

100

What is the slope of a line that is perpendicular to the line 

y = 1/2X + 7?

m = -2

200

What is the equation of a line in GENERAL FORM that is parallel to the line 

y = 1/5 x + 2 

that passes through the origin? 

X - 5Y = 0

300

What is the equation of a line in slope-intercept form that is parallel to the line 

5X - Y - 2 = 0 

and passes through the point f(0) = 4

y = 5x + 4

400

What is the equation of a line in slope-intercept form that is parallel to the x-axis and goes through the point (6,2)?

y = 2

500

Determine an equation in general form, representing a line that is:

- perpendicular to: 

y = 3X + 2/3

- with the same y-intercept as:  

2X - Y - 10 = 0

X + 3Y + 30 = 0

Factoring

100

Fully factor the following expression:

x²+7x+12

(x+3)(x+4)

200

Fully factor the following expression:

x²+ x - 90

(x - 9)(x + 10)

300

Fully factor the following expression:

6x²+66x+60

6(x+10)(x+1)

400

Fully factor the following expression:

-18x⁵ + 3x³ - 21x - 9

3(-6x⁵ + x³ - 7x - 3)

500

Fully factor the following expression:

-4x²yz⁷ - 40xyz⁷ - 96yz⁷

-4yz⁷(x+6)(x+4)