SAT Math Heart of Algebra Question Types Cheat Sheet

Key Facts

• Slope is the rate of change, and it is calculated by $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
• Standard form $Ax + By = C$ can be converted to slope-intercept form by solving for $y$.
• Two lines have one solution when their slopes are different, so $m_1 \ne m_2$.
• Two lines have no solution when they have the same slope but different $y$-intercepts, so $m_1 = m_2$ and $b_1 \ne b_2$.
• Two lines have infinitely many solutions when they are the same line, so $m_1 = m_2$ and $b_1 = b_2$.
• When solving an inequality, multiplying or dividing by a negative number reverses the sign, such as $-2x < 6$ becoming $x > -3$.
• A linear function has a constant rate of change, meaning equal changes in $x$ produce equal changes in $y$.

Vocabulary

Linear equation

An equation whose graph is a straight line and whose variables have no exponent greater than $1$.

Slope

The ratio of vertical change to horizontal change, written as $m = \frac{\Delta y}{\Delta x}$.

Y-intercept

The value of $y$ where a line crosses the $y$-axis, which occurs when $x = 0$.

System of equations

A set of two or more equations that are solved together by finding values that satisfy all equations.

Inequality

A mathematical statement that compares expressions using symbols such as $<$, $>$, $\leq$, or $\geq$.

Rate of change

The amount one quantity changes for each $1$-unit increase in another quantity.