Megan is baking cookies. The oven temperature is 125ºF after one minute and 290ºF after four minutes.
Write an equation in slope-intercept form that describes the oven temperature.
To write an equation in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b). The slope is the rate of change of the oven temperature, and the y-intercept is the oven temperature when time (x) is 0.
Given the information:
At t = 1 min, the oven temperature (y) is 125ºF.
At t = 4 mins, the oven temperature (y) is 290ºF.
We can use these two points to calculate the slope (m):
Point 1: (x1, y1) = (1, 125)
Point 2: (x2, y2) = (4, 290)
The slope (m) is calculated by:
m = (change in y) / (change in x)
m = (y2 - y1) / (x2 - x1)
m = (290 - 125) / (4 - 1)
m = 165 / 3
m = 55
Now that we have the slope, we need to find the y-intercept (b). We can use one of the points we have and the slope to solve for b. Let's use Point 1 for this:
y = mx + b
125 = (55)(1) + b
b = 125 - 55
b = 70
Therefore, the equation in slope-intercept form that describes the oven temperature as a function of time is:
y = 55x + 70
where y represents the oven temperature in degrees Fahrenheit and x represents the time in minutes.