# Linear Equations in Two Variables on the SAT: Examples & Practice Source: https://1600.now/sat-skill/linear-equations-two-variables --- Math · Algebra ## Linear Equations in Two Variables A two-variable linear equation describes a line. Rearrange it to read the slope, set one variable to zero to find an intercept, and substitute coordinates to test whether a point lies on it. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Convert standard form into a readable line For $3x+2y=12$, subtract $3x$ and divide by 2: $y=-\frac{3}{2}x+6$. The slope is $-\frac{3}{2}$ and the vertical intercept is 6. Setting $y=0$ in the original equation gives $x=4$, so the horizontal intercept is $(4,0)$. The coefficient of $x$ in standard form is not automatically the slope. If the equation is $A x+B y=C$ with $B\ne0$, the slope is $-\frac{A}{B}$. ### Write a line through a point A line with slope 2 through $(3,7)$ can be written as $y-7=2(x-3)$. Expanding gives $y=2x+1$. Point-slope form lets you use the given point immediately without guessing the intercept. If two points are given, first calculate $m=\frac{y_2-y_1}{x_2-x_1}$. A zero denominator means a vertical line, so use $x=c$ rather than forcing slope-intercept form. ### Compare parallel and perpendicular lines Distinct parallel nonvertical lines have the same slope. A line perpendicular to a line of slope $-\frac{3}{2}$ has slope $\frac{2}{3}$, because the slopes multiply to $-1$. Vertical and horizontal lines are the exception to the reciprocal calculation: $x=4$ is perpendicular to $y=6$. A vertical slope is undefined, not zero. ### Test a coordinate in the original equation The point $(2,3)$ lies on $3x+2y=12$ because $3(2)+2(3)=12$. The point $(3,2)$ does not: it produces 13. Keep the order of coordinates fixed when substituting. If a problem describes a cost constraint with two items, name each variable and its unit before writing the equation. An equation can be algebraically correct while assigning the prices to the wrong items. ### Check your understanding Try it yourself: What is the slope of $4x+2y=10$? · A $4$ B $2$ C $-2$ D $-4$ ### Sample linear equations in two variables questions Linear Equations in Two Variables · Easy: If $y = 2x + 3$ and $x = 0.5$, what is the value of $y$? · A 3 B 4 C 6 D 7.2 - [Open the question and explanation](https://1600.now/bank/math/4ea7592d) Linear Equations in Two Variables · Easy: If $\frac{x}{y}=72$ and $\frac{cx}{6y}=72$, what is the value of $c$? · A $6$ B $12$ C $72$ D $432$ - [Open the question and explanation](https://1600.now/bank/math/7a9c9ae3) Linear Equations in Two Variables · Easy $y = 84(x - 3) + 287$ Which equation is equivalent to the given equation? A $y = 84x + 287$ B $y = 287x + 539$ C $y = 84x + 35$ D $y = 287x + 84$ - [Open the question and explanation](https://1600.now/bank/math/3f4d83d7) ### Practice this skill 1. Convert a line, then find both intercepts from the original equation. 2. Explain parallel and perpendicular relationships using slopes. 3. Check every selected ordered pair by substitution. [Practice linear equations in two variables](https://1600.now/bank/math/skill/Linear%20equations%20in%20two%20variables) [Print the linear equations in two variables worksheet and worked answers](https://1600.now/sat-linear-equations-two-variables-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Linear equations in two variables" in Algebra. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Linear Functions](https://1600.now/sat-skill/linear-functions)** A linear function changes by the same amount for each equal increase in its input. - **[Systems of Linear Equations](https://1600.now/sat-skill/systems-of-linear-equations)** A solution to a system must satisfy both equations. - **[Linear Inequalities](https://1600.now/sat-skill/linear-inequalities)** Solve inequalities like equations, but reverse the comparison when multiplying or dividing by a negative number.