janelys has a part - time job at an ice skating rink selling hot cocoa. she decided to plot the number of…
janelys has a part - time job at an ice skating rink selling hot cocoa. she decided to plot the number of hot cocoas she sold relative to the days high temperature and then draw the line of best fit. based on the line of best fit, how many hot cocoas would you predict janelys to sell if the days high temperature were 56°f?
Answer
Answer:
52
Explanation:
Step1: Find the slope of the line
The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(0,90)$ and $(48,48)$. Then $m=\frac{48 - 90}{48-0}=\frac{- 42}{48}=-\frac{7}{8}$.
Step2: Find the y - intercept
The y - intercept $b$ of the line is the value of $y$ when $x = 0$. From the point $(0,90)$, we know that $b = 90$.
Step3: Write the equation of the line
The equation of a line in slope - intercept form is $y=mx + b$. Substituting $m =-\frac{7}{8}$ and $b = 90$, we get $y=-\frac{7}{8}x+90$.
Step4: Predict the number of hot - cocoas
We want to find $y$ when $x = 56$. Substitute $x = 56$ into the equation $y=-\frac{7}{8}\times56 + 90$. First, calculate $-\frac{7}{8}\times56=-49$. Then $y=-49 + 90=52$.