Graph and Intercepts

Vocabulary flashcards covering slope-intercept form, slope, intercepts, standard form, and graphing concepts from the lecture notes.

Slope-intercept form

The linear equation form y = mx + b, where m is the slope and b is the y-intercept.

Slope (m)

The rate of change of a line; rise over run; determines how steep the line is and the direction (positive up, negative down).

Y-intercept

The point where the line crosses the y-axis; the value of y when x = 0; given by b in y = mx + b.

X-intercept

The point where the line crosses the x-axis; found by setting y = 0 and solving for x.

Ordered pair

An (x, y) pair representing a point on the line; coordinates that satisfy the equation.

Standard form

The linear equation form ax + by = c.

Converting standard form to slope-intercept

Solve for y to get y = (-a/b)x + c/b (assuming b ≠ 0).

Vertical line

A line of the form x = c; slope is undefined and there is no y-intercept.

Horizontal line

A line of the form y = c; slope is 0; crosses the y-axis at (0, c) and generally has no unique x-intercept unless c = 0.

Two points determine a line

Any two distinct points on a line suffice to draw the line; the line is uniquely determined by them.

Checking if a point is on a line

To verify, substitute the point's coordinates into the equation and see if both sides are equal.

Slope as rise over run example

If m = a/b, then move up a units and right b units for each step along the line.

Intercepts to graph a line

Plot the y-intercept (0, b) and the x-intercept (a, 0) and draw the line through them.

Y-intercept from a standard form example

From ax + by = c, set x = 0 and solve for y to get the y-intercept.

X-intercept from a standard form example

From ax + by = c, set y = 0 and solve for x to get the x-intercept.

Undefined slope and vertical lines

Vertical lines (x = c) have undefined slope due to division by zero when computing rise over run.