Hello!
The slope intercept form is y=mx+b, where m is the slope and b is the y-intercept.
First, let's find the y-intercept. This is where the line hits the y-axis. Therefore, it hits at 4 on the y-axis, so our y-intercept is 4.
To find the slope, let's find 2 points on our line. Let's use (0,4) and (2,5). We divide the difference in the y-values by the difference in the x-values as shown below.
Therefore, our slope is 2.
Now we plug these values into our equation.
y=2x+4
I hope this helps!
Answer:
a) It will take Izzy 0.226 hours = 13.6 minutes = 13 minutes 36 seconds to run to school on dashed days.
b) Izzy runs 1.30 miles on dry days.
c) Izzy saves 3 minutes and 12 seconds cutting through the woods.
Step-by-step explanation:
This problem can be solved by a simpe rule of three problem.
a) On rainy days, she runs 1.2 + 0.5 = 1.7 miles.
The problem states that for rainy days, she runs 7.5 miles per hour. We know that in a hour, Izzy will run 7.5 miles. We want to know how long it takes for her to run 1.7 miles. So
1 hour - 7.5 miles
x hours - 1.7 miles
7.5x = 1.7
x = 0.226 hours
It will take Izzy 0.226 hours = 13.6 minutes = 13 minutes 36 seconds to run to school on dashed days.
b) Now we have a right triangle, where the sides are the 1.2 miles and the 0.5miles, and the path through the woods x is the hypotenuse.
So, we apply the pythagorean theorem.
So, Izzy runs 1.30 miles on dry days.
c) The first step for this question is knowing how long it takes for Izzy to run 1.30 miles at 7.50 miles a hour. So:
1 hour - 7.50 miles
x hours = 1.30 miles
7.50x = 1.30
x = 0.173 hours
So, it takes Izzy 0.173 hours = 10.4 minutes = 10 minutes 24 seconds to run through the woods.
13' 36''
-10' 24''
3' 12''
Izzy saves 3 minutes and 12 seconds cutting through the woods.