DCAS Algebraic Reasoning 3

Question 1

A line has a slope of -2 and passes through the point (0, 5). What is its equation?

Accepted Answer

y = -2x + 5

Answer

Using slope-intercept form y = mx + b with slope m = -2 and y-intercept b = 5 gives y = -2x + 5.

Question 2

Which value of x satisfies the inequality 4x - 3 ≤ 9?

Accepted Answer

3

Answer

Solving: add 3 to get 4x ≤ 12, then divide by 4 to get x ≤ 3, so only x = 3 satisfies the inequality.

Question 3

Which of the following is a linear function?

Accepted Answer

y = 2x + 3

Answer

y = 2x + 3 is linear because x is raised only to the first power and its graph is a straight line.

Question 4

A table shows: x = 1 → y = 4; x = 2 → y = 7; x = 3 → y = 10. Which equation fits this pattern?

Accepted Answer

y = 3x + 1

Answer

As x increases by 1, y increases by 3 (slope = 3), and working back gives a y-intercept of 1, so y = 3x + 1.

Question 5

What is the solution to the system of equations: y = 2x and y = x + 4?

Accepted Answer

(4, 8)

Answer

Setting 2x = x + 4 gives x = 4, and substituting back yields y = 2(4) = 8, so the solution is (4, 8).

DCAS - Delaware Comprehensive Assessment System Practice Test