At 82°F, a certain insect chirps at a rate of 61 times per minute, and at 91°F, they chirp 124 times per minute. Write an equation in slope-intercept form that represents the situation.

Accepted Solution

Answer:[tex]y=7x-513[/tex]Step-by-step explanation:Letx----> the temperature in degrees Fahrenheity ---->insect chirping rate in times per minutewe have the ordered pairs(82,61) and (91,124)step 1Find the slopeThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute the values[tex]m=\frac{124-61}{91-82}[/tex] [tex]m=\frac{63}{9}=7[/tex] step 2Find the equation of the linewe know thatThe equation in slope intercept form is equal to[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptwe have[tex]m=7[/tex]  ---> the units are chirps per minute/degree Ftake the point (82,61)substitute and solve for b[tex]61=7(82)+b[/tex][tex]61=574+b[/tex][tex]b=-513[/tex]substitute[tex]y=7x-513[/tex]