SAT Math Master Study Guide: The 800
Path
Section 1: Heart of Algebra (The Linear Powerhouse)
Approx. 19 questions on the SAT
1.1 Understanding Linear Equations
A linear equation represents a constant rate of change. On the SAT, this usually appears as a
word problem involving a "flat fee" and a "per unit rate."
The Standard Slope-Intercept Form:
y=mx+b
● m (The Slope): The "rate of change." If a taxi charges $2.50 per mile, m=2.5.
● b (The y-intercept): The "starting value" or "initial fee." If the taxi has a base fare of
$5.00, b=5.
Point-Slope Form: Useful when you have a point (x1,y1) and a slope m:
y−y1=m(x−x1)
Standard Form:
Ax+By=C
● Pro-Tip: In this form, the slope is always −BA.
1.2 Systems of Linear Equations
The SAT will ask you to find where two lines cross. There are three possible outcomes for a
system:
1. One Solution: The lines have different slopes and intersect at exactly one point (x,y).
2. No Solution: The lines are parallel. They have the same slope but different
y-intercepts.
3. Infinitely Many Solutions: The lines are identical. They have the same slope and the
same y-intercept.
Path
Section 1: Heart of Algebra (The Linear Powerhouse)
Approx. 19 questions on the SAT
1.1 Understanding Linear Equations
A linear equation represents a constant rate of change. On the SAT, this usually appears as a
word problem involving a "flat fee" and a "per unit rate."
The Standard Slope-Intercept Form:
y=mx+b
● m (The Slope): The "rate of change." If a taxi charges $2.50 per mile, m=2.5.
● b (The y-intercept): The "starting value" or "initial fee." If the taxi has a base fare of
$5.00, b=5.
Point-Slope Form: Useful when you have a point (x1,y1) and a slope m:
y−y1=m(x−x1)
Standard Form:
Ax+By=C
● Pro-Tip: In this form, the slope is always −BA.
1.2 Systems of Linear Equations
The SAT will ask you to find where two lines cross. There are three possible outcomes for a
system:
1. One Solution: The lines have different slopes and intersect at exactly one point (x,y).
2. No Solution: The lines are parallel. They have the same slope but different
y-intercepts.
3. Infinitely Many Solutions: The lines are identical. They have the same slope and the
same y-intercept.
