Graphing Linear Equations flashcards

Card 1

What is the graph of an equation in two variables?

The set of all its solutions plotted as points (x, y). For a linear equation it is a straight line.

Card 2

What are three ways to find points on a line?

A table of values, the y-intercept plus the slope, and the x- and y-intercepts.

Card 3

In y = mx + b, which point do you plot first?

The point (0, b), where the line crosses the y-axis. Its y-value b is the y-intercept.

Card 4

How do you find the x-intercept?

Set y = 0 and solve for x.

Card 5

How do you find the y-intercept?

Set x = 0 and solve for y.

Card 6

Find both intercepts of 6x + 2y = 12.

x-intercept 2, so the line crosses the x-axis at (2, 0), from 6x = 12. y-intercept 6, so it crosses the y-axis at (0, 6), from 2y = 12.

Card 7

What does the graph of y = −1 look like?

A horizontal line through (0, −1) with slope 0.

Card 8

What does the graph of x = 6 look like?

A vertical line through (6, 0) with undefined slope.

Card 9

A line has y-intercept −2 and slope 3/4. Name two points on it.

(0, −2), where the line crosses the y-axis, and, going up 3 and right 4, (4, 1).

Card 10

How do you check whether a point is on a line?

Substitute its x and y into the equation. If both sides match, the point is on the line.

Card 11

A line has slope −3. How do you move from one point on it to another?

Write −3 as −3/1: go down 3 and right 1 (or up 3 and left 1).

Card 12

Why plot a third point?

Two points determine the line. The third is a check: if the three do not line up, there is a mistake.

Card 13

A table of values shows y going up by 5 each time x goes up by 1. What is the slope?

5. Slope is the change in y for each 1 step in x.

Card 14

What is the catch when you graph a line through the origin using intercepts?

Both intercepts are 0, so the line crosses both axes at (0, 0) and you only get one point. Find another with a table or the slope.