Slope of a Line and Slope-Intercept Form

A set of vocabulary and concept flashcards covering linear slopes from graphs, slope-intercept form, and standard form conversions.

Slope of a Line

The measure of the steepness and direction of a straight line, denoted by the variable $m$ and calculated as the ratio of vertical change (rise) to horizontal change (run).

Slope-Intercept Form

A linear equation written in the form $y = mx + b$, where $m$ represents the slope of the line and $b$ represents the y-intercept.

y-intercept

The coordinate point where a graph crosses the vertical y-axis, represented by the constant $b$ (at the point $(0, b)$) in slope-intercept form.

Variable $m$

The standard algebraic variable used to represent the numerical slope of a linear equation or graphed line.

Positive Slope

A line that rises from left to right on a coordinate plane, indicating a slope value where $m > 0$.

Negative Slope

A line that falls from left to right on a coordinate plane, indicating a slope value where $m < 0$.

Slope-Intercept Form of $2x + y = 5$

The converted linear equation $y = -2x + 5$, which has a slope of $m = -2$ and a y-intercept of $b = 5$.

Slope-Intercept Form of $x - 2y = 12$

The converted linear equation $y = \frac{1}{2}x - 6$, which has a slope of $m = \frac{1}{2}$ and a y-intercept of $b = -6$.

Slope-Intercept Form of $2x + y = 9$

The converted linear equation $y = -2x + 9$, which has a slope of $m = -2$ and a y-intercept of $b = 9$.

Slope-Intercept Form of $3x - 2y = 8$

The converted linear equation $y = \frac{3}{2}x - 4$, which has a slope of $m = \frac{3}{2}$ and a y-intercept of $b = -4$.

Linear Equation with Slope $-3$ and y-intercept $5$

The equation $y = -3x + 5$, describing a line with a negative rate of change of $-3$ that intersects the y-axis at $(0, 5)$.

Linear Equation with Slope $-\frac{1}{4}$ and y-intercept $3$

The equation $y = -\frac{1}{4}x + 3$, describing a line that decreases by $1$ unit vertically for every $4$ units horizontally and passes through $(0, 3)$.

Linear Equation with Slope $-2$ and y-intercept $1$

The equation $y = -2x + 1$, describing a line that falls $2$ units for every $1$ unit of horizontal increase and intersects the y-axis at $(0, 1)$.

Linear Equation with Slope $-5$ and y-intercept $6$

The equation $y = -5x + 6$, describing a steep line falling at a rate of $-5$ that crosses the y-axis at $(0, 6)$.

Linear Equation $y = 5x + 2$

A line expressed in slope-intercept form having a positive slope of $m = 5$ and crossing the y-axis at $b = 2$.

Linear Equation $y = \frac{1}{3}x - 3$

A line expressed in slope-intercept form having a slope of $m = \frac{1}{3}$ and crossing the y-axis at $b = -3$.