Question

Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation.

y = 2x + 5
y = 4x + 8
f(x) = 2x + 5
f(x) = 4x + 8

Answer 1

find the slope
(y2-y1)/(x2-x1)=slope
(15-7)/(5-1)=8/4=2
slope is 2

either 1st or 3rd
function notaiton seems to be f(x)

3rd otpion is answer
f(x)=2x+5

Answer 2

Option C is correct.

The equation of line is , f(x)=2x+5

Explanation:

Point slope intercept form: For any two points
`(x_1, y_1)` and
`(x_2, y_2)` then,

the general form of the equation of line is given by;

`y-y_1=m(x-x_1)`; where m is the slope given by:

`m=(y_2-y_1)/(x_2-x_1)`

Consider the given points;

(1, 7) and (5 , 15)

First calculate the slope (m);

`m=(y_2-y_1)/(x_2-x_1) =(15-7)/(5-1) =(8)/(4) =2`

Therefore, slope of the line, m=2

Then, the equation of line is:

`y-y_1=m(x-x_1)`

Substitute the value of m=2 and (1, 7) above we get;

`y-7=2(x-1)`

or

`y-7=2x-2`

Add 7 to both sides of an equation we get;

`y-7+7=2x-2+7`

Simplify:

`y=2x+5`

using function notation i.e, y =f(x)

then, we have f(x) = 2x+5

therefore, the equation of line that passes through the point (1, 7) and (5, 15) is ; f(x)=2x+5