Question

At 107°F, a certain insect chirps at a rate of 92 times per minute, and at 113°F, they chirp 116 times per minute. Write an equation in slope-intercept form that represents the situation.

Answer 1

Answer:

The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.

Step-by-step explanation:

A linear equation can be expressed in the form y=m*x + b. In this equation, x and y are coordinates of a point, m is the slope and b is the y coordinate of the y-intercept. Since this equation describes a line in terms of its slope and its y-intercept, this equation is said to be in its slope-intercept form.

When there are two points of a line (x1, y1) and (x2, y2), the slope is determined by the quotient between the difference of the ordinate of these two points and the difference of the abscissa of the same points. This is:

$m=\frac{y2-y1}{x2-x1}$

Having a point on the line, you can substitute the values ​​of m, x and y in the equation y = mx + b and thus find b.

In this case:

• (x1, y1): (92, 107)
• (x2, y2): (116, 113)

So:

$m=\frac{113-107}{116-92}$

m= 0.25

substituting the values ​​of m, x1 and y1 in the equation y = mx + b you have:

107= 0.25*92 + b

107 - 0.25*92= b

84=b

The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.