Question

question 9 short answer system 9: y = 0.25x - 3 y = 0.25x + 2 list the slope (m) and y-intercept (b) for each equation. determine the type of system and explain your reasoning. write your short answer response...

Explanation:

Step1: Identify slope-intercept form

The slope-intercept form is $y = mx + b$, where $m$ = slope, $b$ = y-intercept.

Step2: Extract values for first equation

For $y = 0.25x - 3$:
Slope $m = 0.25$, y-intercept $b = -3$

Step3: Extract values for second equation

For $y = 0.25x + 2$:
Slope $m = 0.25$, y-intercept $b = 2$

Step4: Classify the system

Parallel lines have equal slopes, different intercepts, and no intersection. Since the two equations have identical slopes but distinct y-intercepts, they represent parallel lines with no solution.

Answer:

1. For $y = 0.25x - 3$:

Slope ($m$) = $0.25$, y-intercept ($b$) = $-3$

1. For $y = 0.25x + 2$:

Slope ($m$) = $0.25$, y-intercept ($b$) = $2$

This is an inconsistent system of linear equations. The two lines have identical slopes but different y-intercepts, meaning they are parallel and never intersect, so there is no solution to the system.