write an equation that is perpendicular to x - 3y =3 and passes through the point (5,-9) in slope-intercept form.
1 answer:
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Answer:
y = -3x +6
Step-by-step explanation:
The perpendicular line will have the coefficients of x and y swapped (and one of them negated), and will have a constant appropriate to the point the line needs to go through.
The equation will look like ...
x -3y = 3 . . . . . . . . . . . . . given line
3x +y = constant . . . . . . perpendicular line
where "constant" can be found by substituting for x and y.
3x +y = 3(5) +(-9)
3x +y = 6 . . . . equation in standard form
To put this in slope-intercept form subtract 3x:
y = -3x +6
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- <em>On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population increases by a factor of 5 every 2 days, and can be modeled by a function, L, which depends on the amount of time, t (in days). Before the first day of spring, there were 7600 locusts in the population. Write a function that models the locust population t days since the first day of spring.</em>
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<h2>Solution</h2>A function that grows with a constant factor is modeled by an exponential function of the kind:
Where A is the initial value, B is the constant growing factor, and x is the number of times the growing factor applies.
Since the population increases by a factor of 5 every 2 days, the power x of the exponential function is t/2, and the factor B is 5.
The initial popultaion A is 7600.
Thus, the function that models the locust population t days since the first day of spring is: