Question

1. what is the slope of the line in the equation $3x - y = 7$?

a. $-3$
b. $3$
c. $\frac{1}{3}$
d. $-\frac{1}{3}$

1. if a system of equations is represented by two lines with the same slope but different y-intercepts, what can be said about the system?

a. the system has one unique solution.
b. the system cannot be determined.
c. the system has no solution.
d. the system has infinitely many solutions.

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $3x - y = 7$ to $y = 3x - 7$.

Step2: Identify slope from the form

For $y=mx+b$, slope $m=3$.

Step1: Analyze line properties

Same slope means parallel lines.

Step2: Determine solution status

Parallel lines with different y-intercepts never intersect, so no solution.

Answer:

1. b. 3
2. c. The system has no solution.