Please help quick! its for a unit test, i cant get it wrong

She leaves her house after 10 minutes.

Step-by-step explanation:

Because she rides at a constant speed, we know that the data in the table represents a linear relation.

Remember that a linear relation can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

For a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have 3 points of the line, we must only use two of them, for example, we can use the first two:

(6km, 46min)

(8km, 58 min)

Then the slope is:

a = (58min - 46min)/(8km - 6km) = 6 min/km

Then the equation is something like:

y = ( 6 min/km)*x + b

to find the value of b, we can use the first point  (6km, 46min), this means that when x = 6km, we must have y = 46min

then:

46 min = (6min/km)*6km + b

46min = 36min  + b

46min - 36min = b = 10 min

Then the equation is:

y = (6min/km)*x + 10min

When she leaves her house, her position is still 0km, so evaluating the function in that value we get:

y = (6min/km)*0km + 10min

y = 10min

She leaves her house after 10 minutes.