Algebra: Graphs flashcards

Question 1

What is the point (0, 0) called?

Accepted Answer

The origin, where the x-axis and y-axis cross.

Question 2

Into how many quadrants do the x-axis and y-axis divide the plane?

Accepted Answer

Four.

Question 3

What are the signs of (x, y) in Quadrant I?

Accepted Answer

(+, +)

Question 4

What are the signs of (x, y) in Quadrant II?

Accepted Answer

(−, +)

Question 5

What are the signs of (x, y) in Quadrant III?

Accepted Answer

(−, −)

Question 6

What are the signs of (x, y) in Quadrant IV?

Accepted Answer

(+, −)

Question 7

What is the y-coordinate of every point on the x-axis?

Accepted Answer

0; such points have coordinates (a, 0).

Question 8

What is the x-coordinate of every point on the y-axis?

Accepted Answer

0; such points have coordinates (0, b).

Question 9

What is the standard form of a linear equation in two variables?

Accepted Answer

Ax + By = C, with A and B not both equal to zero.

Question 10

What shape is the graph of Ax + By = C?

Accepted Answer

A straight line; its points are exactly the solutions of the equation.

Question 11

What are the intercepts of a line?

Accepted Answer

The points where it meets the x-axis and where it meets the y-axis.

Question 12

How do you find the x-intercept from a line's equation?

Accepted Answer

Set y = 0 and solve for x.

Question 13

How do you find the y-intercept from a line's equation?

Accepted Answer

Set x = 0 and solve for y.

Question 14

What kind of line is the graph of y = b?

Accepted Answer

A horizontal line, crossing the y-axis at (0, b).

Question 15

What kind of line is the graph of x = a?

Accepted Answer

A vertical line, crossing the x-axis at (a, 0).

Question 16

In terms of rise and run, what is the slope m of a line?

Accepted Answer

m = rise / run.

Question 17

What is the rise of a line?

Accepted Answer

Its vertical change.

Question 18

What is the run of a line?

Accepted Answer

Its horizontal change.

Question 19

What is the slope of the line through (x1, y1) and (x2, y2)?

Accepted Answer

m = (y2 − y1) / (x2 − x1)

Question 20

Which way does a line with positive slope go, read from left to right?

Accepted Answer

Up.

Question 21

Which way does a line with negative slope go, read from left to right?

Accepted Answer

Down.

Question 22

What is the slope of a horizontal line?

Accepted Answer

0

Question 23

What is the slope of a vertical line?

Accepted Answer

Undefined.

Question 24

What is the slope–intercept form of a line with slope m and y-intercept (0, b)?

Accepted Answer

y = mx + b

Question 25

What is the point–slope form of a line with slope m through (x1, y1)?

Accepted Answer

y − y1 = m(x − x1)

Question 26

What are parallel lines?

Accepted Answer

Coplanar lines that never intersect.

Question 27

How do the slopes m1 and m2 of two parallel lines compare?

Accepted Answer

They are equal: m1 = m2.

Question 28

What are perpendicular lines?

Accepted Answer

Coplanar lines that meet at a right angle.

Question 29

When is the boundary line of a linear inequality drawn solid?

Accepted Answer

When the inequality is ≤ or ≥.

Question 30

When is the boundary line of a linear inequality drawn dashed?

Accepted Answer

When the inequality is < or >.

Algebra: Graphs flashcards

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