Mathfolis

Linear Equations in Two Variables

Unit 1 · Algebra

What the SAT asks here

A linear equation in two variables describes infinitely many (x, y) pairs that lie on a single line. The SAT uses three common forms, and you'll be expected to move between them on demand. Average frequency is about two problems per test.

Three useful forms

Slope-intercept
y=mx+by = mx + b
Standard
Ax+By=CAx + By = C
Point-slope (given point (x1,y1)(x_1, y_1) and slope m)
y−y1=m(x−x1)y - y_1 = m(x - x_1)

Standard → slope-intercept

Solve Ax + By = C for y
y=−ABx+CBy = -\frac{A}{B}x + \frac{C}{B}
SAT Tip: If the answer choices are already in slope-intercept form, convert the given equation first — it's almost always faster than trying to match standard forms directly.
Caution: When you move Ax to the other side of Ax + By = C, the sign flips. Then dividing by B may flip it again — track signs deliberately.
Type 1

Convert between forms

Rearrange algebraically. The most common SAT version is standard → slope-intercept: solve for y and read off m and b.

Example 1
Rewrite the equation 4x − 2y = 10 in slope-intercept form.

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Type 2

Write an equation from given information

Use point-slope if you have a point and a slope; convert to slope-intercept if the answer choices demand it.

Example 2
A line has slope −4 and passes through (1, 3). Write the equation of the line in slope-intercept form.

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Type 3

Find values that satisfy an equation

Substitute the known coordinate(s) and solve for the unknown variable or coefficient.

Example 3
If the point (2, k) lies on the line 3x − 5y = 16, what is the value of k?

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Linear Equations in Two Variables | SAT Math — Mathfolis