Question

7. Christa's friend Edrei takes the bus to school. She starts at a distance of 8 miles from the school. After 10 minutes on the bus, she is 4 miles from the school. After 20 minutes, she is O miles from the school. Use the steps to find the equation that describes Edrei's distance from school as she rides the bus.1. find the slope of the line using the points 10, 4 and 20, 02. identify the starting value b3. write the equation that represents this situation in the form y = mx + b

Answer 1

She start at a dirtance of 8 miles from the school, and after 10 minutes she is 4 miles from the school. so that means that in 10 minutes she advance halve of the way so we can find the ratio that will be:

$\frac{10}{4}=\frac{5}{2}$

Now we can multiply the ratio for a number that give you the 20 minutes so in this case us 4

$\frac{5\cdot4}{2\cdot4}=\frac{20}{8}$

So after 20 minutes she arrive to the school, now let's find the slope:

we know that the equation is:

$m=\frac{y_2-y_1}{x_2-x_1}$

and we replace the coordinates so:

$m=\frac{0-4}{20-10}=-\frac{4}{10}=-\frac{2}{5}$

now the starting point or the intercection with the y coordinate will be (0,8) because he start at 0 miles and the time is 0 so the final equation will be:

$y=-\frac{2}{5}x+8$