lily has $45 in her school lunch account. if she spends $2.50 each day, which graph represents lily’s account balance, y, after she buys lunch for x days?

a.

graph a: account balance ($) on y - axis, days on x - axis. y - axis from 0 to 50, x - axis from 0 to 20. line starts at (0, 45) and goes to (20, 5)? wait, no, looking at the grid: when x = 0, y = 45? wait, the first graph: x - axis labels 0, 4, 8, 12, 16, 20. y - axis 0, 10, 20, 30, 40, 50. the line in a: at x = 0, y is 45? wait, the grid: each square maybe 5? wait, the first graph: when x = 0, y is 45 (since 45 is between 40 and 50, closer to 45? wait, the second graph b: at x = 16, y = 0? wait, lets re - express:

graph a: x - axis (days) 0, 4, 8, 12, 16, 20. y - axis (account balance $) 0, 10, 20, 30, 40, 50. the line in a: when x = 0, y = 45? wait, no, the first graphs line: at x = 0, y is 45 (since 45 is 9 units of 5? wait, maybe each grid square is 5. so x = 0, y = 45; x = 4, y = 35; x = 8, y = 25; x = 12, y = 15; x = 16, y = 5; x = 20, y = - 5? no, that cant be. wait, maybe the initial balance is $45, daily spending $2.50. so the equation is y = 45 - 2.5x. lets find when y = 0: 45 - 2.5x = 0 → 2.5x = 45 → x = 18. so the x - intercept should be at x = 18. wait, graph a: x - axis up to 20, and at x = 20, y is 5? wait, maybe i misread. wait, the users image:

graph a: x - axis (days) 0, 4, 8, 12, 16, 20. y - axis (account balance $) 0, 10, 20, 30, 40, 50. the line in a: starts at (0, 45) (since 45 is between 40 and 50, 45 - 2.5*4 = 45 - 10 = 35 (x = 4, y = 35), 45 - 2.5*8 = 45 - 20 = 25 (x = 8, y = 25), 45 - 2.5*12 = 45 - 30 = 15 (x = 12, y = 15), 45 - 2.5*16 = 45 - 40 = 5 (x = 16, y = 5), 45 - 2.5*20 = 45 - 50 = - 5 (but y cant be negative, so maybe the line is drawn to x = 20, but the actual domain is x from 0 to 18).

graph b: x - axis 0, 4, 8, 12, 16, 20. y - axis 0, 10, 20, 30, 40, 50. the line in b: starts at (0, 45) and goes to (16, 0). lets check the slope: (0 - 45)/(16 - 0) = - 45/16 ≈ - 2.8125, but the daily spending is $2.50, so slope should be - 2.5. so graph a has a slope of - 2.5 (since from x = 0 to x = 4, y goes from 45 to 35: (35 - 45)/(4 - 0) = - 10/4 = - 2.5). graph b: from x = 0 to x = 4, y goes from 45 to 35? wait, no, maybe my initial reading is wrong. anyway, the ocr text is: lily has $45 in her school lunch account. if she spends $2.50 each day, which graph represents lily’s account balance, y, after she buys lunch for x days?

options a and b with their graphs.

Question

lily has $45 in her school lunch account. if she spends $2.50 each day, which graph represents lily’s account balance, y, after she buys lunch for x days?

a.

graph a: account balance ($) on y - axis, days on x - axis. y - axis from 0 to 50, x - axis from 0 to 20. line starts at (0, 45) and goes to (20, 5)? wait, no, looking at the grid: when x = 0, y = 45? wait, the first graph: x - axis labels 0, 4, 8, 12, 16, 20. y - axis 0, 10, 20, 30, 40, 50. the line in a: at x = 0, y is 45? wait, the grid: each square maybe 5? wait, the first graph: when x = 0, y is 45 (since 45 is between 40 and 50, closer to 45? wait, the second graph b: at x = 16, y = 0? wait, lets re - express:

graph a: x - axis (days) 0, 4, 8, 12, 16, 20. y - axis (account balance $) 0, 10, 20, 30, 40, 50. the line in a: when x = 0, y = 45? wait, no, the first graphs line: at x = 0, y is 45 (since 45 is 9 units of 5? wait, maybe each grid square is 5. so x = 0, y = 45; x = 4, y = 35; x = 8, y = 25; x = 12, y = 15; x = 16, y = 5; x = 20, y = - 5? no, that cant be. wait, maybe the initial balance is $45, daily spending $2.50. so the equation is y = 45 - 2.5x. lets find when y = 0: 45 - 2.5x = 0 → 2.5x = 45 → x = 18. so the x - intercept should be at x = 18. wait, graph a: x - axis up to 20, and at x = 20, y is 5? wait, maybe i misread. wait, the users image:

graph a: x - axis (days) 0, 4, 8, 12, 16, 20. y - axis (account balance $) 0, 10, 20, 30, 40, 50. the line in a: starts at (0, 45) (since 45 is between 40 and 50, 45 - 2.5*4 = 45 - 10 = 35 (x = 4, y = 35), 45 - 2.5*8 = 45 - 20 = 25 (x = 8, y = 25), 45 - 2.5*12 = 45 - 30 = 15 (x = 12, y = 15), 45 - 2.5*16 = 45 - 40 = 5 (x = 16, y = 5), 45 - 2.5*20 = 45 - 50 = - 5 (but y cant be negative, so maybe the line is drawn to x = 20, but the actual domain is x from 0 to 18).

graph b: x - axis 0, 4, 8, 12, 16, 20. y - axis 0, 10, 20, 30, 40, 50. the line in b: starts at (0, 45) and goes to (16, 0). lets check the slope: (0 - 45)/(16 - 0) = - 45/16 ≈ - 2.8125, but the daily spending is $2.50, so slope should be - 2.5. so graph a has a slope of - 2.5 (since from x = 0 to x = 4, y goes from 45 to 35: (35 - 45)/(4 - 0) = - 10/4 = - 2.5). graph b: from x = 0 to x = 4, y goes from 45 to 35? wait, no, maybe my initial reading is wrong. anyway, the ocr text is: lily has $45 in her school lunch account. if she spends $2.50 each day, which graph represents lily’s account balance, y, after she buys lunch for x days?

options a and b with their graphs.

Accepted Answer

# Explanation:
## Step1: Find the equation of the line
The initial balance (when $ x = 0 $) is $ y = 45 $, so the y - intercept $ b = 45 $. The rate of change (slope $ m $) is the amount spent per day, which is $ - 2.50 $ (negative because the balance is decreasing). The equation of the line is $ y=-2.5x + 45$.

## Step2: Find the x - intercept (when $ y = 0 $)
Set $ y = 0 $ in the equation $ 0=-2.5x + 45 $.
Add $ 2.5x $ to both sides: $ 2.5x=45 $.
Divide both sides by $ 2.5 $: $ x=\frac{45}{2.5}=18 $. So the line should cross the x - axis at $ x = 18 $.

## Step3: Analyze the graphs
- For option A: When $ x = 20 $, let's check the y - value. Using the equation $ y=-2.5\times20 + 45=-50 + 45=-5 $, but the graph in A at $ x = 20 $ has $ y = 5 $ (positive), but we can also check the x - intercept. From the graph, when $ y = 0 $, $ x\approx18 $ (since $ 45\div2.5 = 18 $). Wait, let's recalculate the x - intercept correctly. $ 45\div2.5=\frac{45}{\frac{5}{2}}=45\times\frac{2}{5}=18 $. So the x - intercept is at $ x = 18 $.
- For option B: The x - intercept is at $ x = 16 $, which would mean $ 2.5\times16 = 40
eq45 $, so it's incorrect.

Wait, let's re - evaluate. The initial balance is $ \$45 $, and she spends $ \$2.50 $ per day. The number of days she can buy lunch is $ 45\div2.5 = 18 $ days. So the graph should have a y - intercept of 45 and an x - intercept of 18.

Looking at graph A: When $ x = 0 $, $ y = 45 $ (correct), and when $ y = 0 $, $ x = 18 $ (since $ 45\div2.5 = 18 $). Let's check the slope. The slope is $ - 2.5 $. From $ x = 0,y = 45 $ to $ x = 4,y = 45-2.5\times4=45 - 10 = 35 $. In graph A, at $ x = 4 $, $ y = 35 $ (correct). At $ x = 8 $, $ y=45-2.5\times8 = 45 - 20 = 25 $. In graph A, at $ x = 8 $, $ y = 25 $ (correct). At $ x = 12 $, $ y=45-2.5\times12=45 - 30 = 15 $. In graph A, at $ x = 12 $, $ y = 15 $? Wait no, the first graph (A) at $ x = 12 $ has $ y = 20 $? Wait, maybe I misread the graph. Wait the first graph (A) has at $ x = 0 $, $ y = 45 $; at $ x = 4 $, $ y = 35 $; at $ x = 8 $, $ y = 25 $; at $ x = 12 $, $ y = 15 $; at $ x = 16 $, $ y = 5 $; at $ x = 18 $, $ y = 0 $. Wait $ 2.5\times18=45 $, so at $ x = 18 $, $ y = 0 $. Let's check the second graph (B): at $ x = 0 $, $ y = 45 $; at $ x = 4 $, $ y = 35 $; at $ x = 8 $, $ y = 25 $; at $ x = 12 $, $ y = 15 $; at $ x = 16 $, $ y = 0 $. But $ 2.5\times16 = 40
eq45 $, so graph B is wrong. Graph A: $ 2.5\times18 = 45 $, so when $ x = 18 $, $ y = 0 $, which is correct.

# Answer:
A. The graph with y - intercept 45, x - intercept 18, and a slope of - 2.5 (representing the daily decrease in balance).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find the equation of the line

Step2: Find the x - intercept (when \( y = 0 \))

Step3: Analyze the graphs

Answer: