Use the image to answer the question.
A line graph shows time in weeks on the x-axis and total in dollars on the y-axis. The x-axis ranges from 0 to 8 in increments of 1. The y-axis ranges from 0 to 160 in increments of 20. A line starts at the origin and passes through plotted points left parenthesis 2 comma 50 right parenthesis; left parenthesis 3 comma 75 right parenthesis; and left parenthesis 4 comma 100 right parenthesis.
Miley is saving for a new pair of boots. They cost $150 . Every week, she puts $25 into her savings account. Based on the graph, state the number of weeks it will take for her to save enough money to buy the boots.
(1 point)
weeks
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Based on the graph, Miley saves $25 per week. The line on the graph passes through the point (4, 100) which represents 4 weeks and $100 saved. Since Miley needs $150 to buy the boots, she needs to save an additional $50. Since she saves $25 per week, it will take her 2 additional weeks to save enough money to buy the boots. Therefore, it will take Miley 6 weeks to save enough money to buy the boots.
To determine the number of weeks it will take Miley to save enough money to buy the boots, we need to find the point on the graph where the total amount equals or exceeds $150.
From the given information, we can see that the line passes through points (2, 50), (3, 75), and (4, 100).
Since the line starts at the origin and the increments on the x-axis are 1, we can determine that the y-intercept of the line (where x = 0) is 0.
To find the equation of the line, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the line using the points (2, 50) and (4, 100):
Slope (m) = (100 - 50) / (4 - 2) = 50 / 2 = 25
Now that we have the slope, we can write the equation of the line:
y = 25x + b
To find the value of b (the y-intercept), we can substitute the coordinates of any point on the line into the equation and solve for b. Let's use the point (2, 50):
50 = 25(2) + b
50 = 50 + b
b = 50 - 50
b = 0
So the equation of the line is y = 25x.
To determine the number of weeks it will take Miley to save enough money to buy the boots, we need to find the x-coordinate of the point where y = $150.
150 = 25x
Divide both sides of the equation by 25:
x = 150/25
x = 6
Therefore, it will take Miley 6 weeks to save enough money to buy the boots based on the graph.
To answer this question using the given line graph, we need to determine where the line representing Miley's savings intersects with the line representing the cost of the boots.
Looking at the graph, we can see that Miley starts at the origin (0,0) and after 2 weeks, she has saved $50 (2,50). After 3 weeks, she has saved $75 (3,75), and after 4 weeks, she has saved $100 (4,100).
Now we need to determine how many weeks it will take for Miley to save enough money to buy the boots, which cost $150. Since she saves $25 per week, we can see that after 5 weeks, she will have saved $125 (5,125), and after 6 weeks, she will have saved $150 (6,150).
Therefore, it will take Miley 6 weeks to save enough money to buy the boots.