Linear Equations

Question 0

What are two ways of determining slope?

Answer 0

1. Counting rise(y) and run(x) on a graph (x,y)

2. m= y2-y1/x2-x1

Question 1

What is the standard algebraic firm for linear equations?

Answer 1

y=mx+b

m=slope rise/run
b= y intercept

(x,y) are ordered pairs

Question 2

What slope do horizontal lines have?

Answer 2

They have a slope of zero, therefore the “mx” disappears. y= b

Question 3

What slope do vertical lines have?

Answer 3

They are undefined. x=n, where n is the x-intercept

Question 4

For parallel lines, what is the relationship between the slopes?

Answer 4

They are the same. These lines will never cross.

Ex: y= 3x + 1
y= 3x + 3

Question 5

What is the relationship between slopes if perpendicular lines?

Answer 5

They are negative reciprocals of each other.

Ex: y= -3x + 7
y= 1/3x -12

Question 6

What are the steps for graphing a line from an equation?

Answer 6

1. Mark y-intercept (b) on graph
2. Starting from y- intercept, count out the slope (rise(y)/run(x) and remember negative signs)
3. Mark the point you reach after counting slope
4. Connect two points with a line

Question 7

What is shown by this equation?

2x+3y=12

Answer 7

This shows the x and y intercept.

To solve for x-intercept, let y= 0. You’ll have (x,0)

To solve for y-intercept, let x= 0. You’ll have (0,y)

Then just graph both points and draw line

Question 8

What are two ways of writing linear equations from graphs?

Answer 8

If y-intercept is clearly evident, use it as (b) and then count the slope (rise/run) from there to another clearly defined point

If y-intercept is unclear, calculate slope of two clearly defined points (m=y2-y1/x2-x1) then use one of the points to solve for y-intercept (b)

Question 9

What type of line should be used when graphing a linear inequality using a greater than or equal to symbol?

Answer 9

A solid line

Question 10

What type of line should be used when graphing a linear inequality using a greater than symbol?

Answer 10

A dotted line

Question 11

How do you determine where to shade when graphing linear inequalities?

Answer 11

Plug in (0,0) for the equation and if true, shade the side if the line containing the point (0,0), if false, shade the opposite side

Question 12

What are the two differences when graphing linear inequalities as opposed to linear equations?

Answer 12

1. The line drawn can be either solid it dotted

2. One side of the graph is shaded to show range of answers

Question 13

What is a system of equations?

Answer 13

A group of two or more linear equations. Has either one solution where lines intersect( given as an ordered pair x,y), or no solution because lines are parallel

To solve