Question

1. identify the equation of the line graphed below. prove by converting!

neg slope= $ax + by = c$
pos slope= $ax - by = c$
a. $2x + y = 4$
b. $2x - y = 4$
c. $x + 2y = 8$
d. $x - 2y = 8$

1. identify the equation of the line graphed below. prove by converting!

a. $3x + 5y = 5$
b. $3x - 5y = 5$
c. $5x + 3y = 3$
d. $5x - 3y = 3$
topic 4: x- and y-intercepts plug 0 in for x

1. $4x - y = 4$
2. $12x - 8y = 24$

Explanation:

Problem 12

Step1: Find slope-intercept form

Convert options to $y=mx+b$:

• A: $y=-2x+4$ ($m=-2, b=4$)
• B: $y=2x-4$ ($m=2, b=-4$)
• C: $y=-\frac{1}{2}x+4$ ($m=-\frac{1}{2}, b=4$)
• D: $y=\frac{1}{2}x-4$ ($m=\frac{1}{2}, b=-4$)

Step2: Match graph features

Graph has negative slope, y-intercept $4$. Only option A matches.

Step1: Find slope-intercept form

Convert options to $y=mx+b$:

• A: $y=-\frac{3}{5}x+1$ ($m=-\frac{3}{5}, b=1$)
• B: $y=\frac{3}{5}x-1$ ($m=\frac{3}{5}, b=-1$)
• C: $y=-\frac{5}{3}x+1$ ($m=-\frac{5}{3}, b=1$)
• D: $y=\frac{5}{3}x-1$ ($m=\frac{5}{3}, b=-1$)

Step2: Match graph features

Graph has positive slope, y-intercept $-1$, slope $\frac{3}{5}$. Only option B matches.

Step1: Find x-intercept (set $y=0$)

$4x - 0 = 4 \implies x=1$

Step2: Find y-intercept (set $x=0$)

$0 - y = 4 \implies y=-4$

Answer:

A. $2x + y = 4$

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Problem 13