Question

What function describes a line with slope 4/3 and passing through the point (2,5) ?

Answer 1

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the data given we have:

`m = \frac {4} {3}`

Thus, the equation is of the form:

`y = \frac {4} {3} x + b`

We substitute the given point and find the cut point "b":

`(x, y) :( 2,5)`

So:

`5 = \frac {4} {3} (2) + b\\5 = \frac {8} {3} + b\\5- \frac {8} {3} = b\\b = \frac {3 * 5-8} {3}\\b = \frac {15-8} {3}\\b = \frac {7} {3}`

Thus, the equation is:

`y = \frac {4} {3} x + \frac {7} {3}`

Finally, we have that the function is of the form
`y = f (x)`, where
`f (x) = \frac {4} {3} x + \frac {7} {3}`

ANswer:

The function that describes the line is:
`f (x) = \frac {4} {3} x + \frac {7} {3}`