Last week, arnold purchased 3 apples at the store for $3.90. this week he purchased 5 apples for $6.50. arnold analyze the price of apples. be sure to include at least three vocabulary words in your responses. plot both of these points on a coordinate plane. draw a line that passes through both of these points: write an equation, in slope-intercept form, that shows the relationship between the number of apples purchased and the total price. describe the relationship between the slope of the line and the rate? what rate is being measured? what is the y-intercept of this equation? what does this y-intercept tell you about this equation? what kind of relationship do the two quantities (the number of apples and the amount of money) have? answer all of these questions in detail for the branilest answer

Apple→x
3x=$3.90 and 5x=$6.50⇒cost of one apple is $3.90/3 and $6.50/5 so the price of one apple is $1.30.

For the plot has two points: (3,3.90) and (5,6.50). I am attaching the picture of the plot.

To write an equation, for this case, we can use two points that we have, (3,3.90) and (5,6.50) and find the equation of the line that passes through the points.
y→total price
x→number of apples
(y-y₁)/(y₂-y₁)=(x-x₁)/(x₂-x₁)
(y-3.90)/(6.50-3.90)=(x-3)/(5-3)⇒(y-3.90)/2.6=(x-3)/2
2*(y-3.90)=2.6*(x-3)⇒2y-7.8=2.6x-7.8
2y=2.6x
y=1.3x→equation in slope-intercept form that shows the relationship between the number of apples purchased and the total price.

We know, from looking at our graph, that the number of apples is out x coordinate and total price of apples purchased is our y coordinate. We have two order of pairs and equation of the line that shows the relationship between the number of apples purchased and the total price.
Slope is 1.3 so the rate is $1.3 per apple purchased. Therefore, Arnold spend $1.3 per apple.

y=mx+b, where m is slope of the line and b the y coordinate of the y intercept
Equation for this case is y=1.3x or y=1.3x+0 so y-intercept of this equation is 0.


y-intercept of this equation is 0, this means that the line goes through the y axis (x = 0) at the 0 mark. The line passes through the origin.
The number of apples and the amount of money have linear relationship.

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