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) weeksSkip to navigation
Based on the graph, it will take Miley 6 weeks to save enough money to buy the boots.
Based on the graph, you can determine the number of weeks it will take for Miley to save enough money to buy the boots by finding the point where the line intersects with the y-coordinate of $150.
From the graph, we can see that the line passes through the point (4, 100) and that the y-axis has increments of 20. Therefore, the line will pass through the y-coordinate of $150 at some point between weeks 4 and 5.
Since Miley saves $25 every week, it will take her 6 weeks (4 + 2) to save enough money to buy the boots.
To answer the question using the given line graph, we need to determine the point on the graph where the line reaches or exceeds $150, which represents the cost of the boots.
Looking at the plotted points on the graph, we see that the line starts at the origin (0,0) and passes through the points (2,50), (3,75), and (4,100).
To find the slope of the line, we can use the formula:
slope = (change in y) / (change in x)
Using the point (2,50) and (3,75), the change in y is 75 - 50 = 25, and the change in x is 3 - 2 = 1. Therefore, the slope is 25 / 1 = 25.
Now we can use the slope-intercept form of a linear equation to find the equation of the line:
y = mx + b
Using the point (2,50), we substitute the values into the equation:
50 = 25(2) + b
Simplifying, we have:
50 = 50 + b
b = 50 - 50 = 0
Therefore, the equation of the line is y = 25x.
Now we can determine the number of weeks it will take for Miley to save enough money to buy the boots, which is represented by $150.
Using the equation y = 25x and substituting y = 150, we have:
150 = 25x
Dividing both sides by 25, we get:
6 = x
Therefore, it will take Miley 6 weeks to save enough money to buy the boots.