Question

question
a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. based on the line of best fit, how many times would the cricket most likely chirp per minute if the temperature outside were $77^\circ f$
temperature (degrees fahrenheit)
chirps per minute

Explanation:

Step1: Define line equation form

We use the linear equation $y = mx + b$, where $y$ = temperature (°F), $x$ = chirps per minute, $m$ = slope, $b$ = y-intercept.

Step2: Calculate slope from two points

Use points $(133,71)$ and $(126,69)$.
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{71 - 69}{133 - 126} = \frac{2}{7}$

Step3: Solve for y-intercept $b$

Substitute $m=\frac{2}{7}$, $x=133$, $y=71$ into $y=mx+b$:
$71 = \frac{2}{7}(133) + b$
$71 = 38 + b$
$b = 71 - 38 = 33$

Step4: Write full linear equation

$y = \frac{2}{7}x + 33$

Step5: Solve for $x$ when $y=77$

Substitute $y=77$ into the equation:
$77 = \frac{2}{7}x + 33$
$77 - 33 = \frac{2}{7}x$
$44 = \frac{2}{7}x$
$x = 44 \times \frac{7}{2} = 154$

Answer:

154 chirps per minute