Question

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

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

Answer:

Option C is correct.

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

Step-by-step 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:

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

Consider the given points;

(1, 7) and (5 , 15)

First calculate the slope (m);

$m=\frac{y_2-y_1}{x_2-x_1} =\frac{15-7}{5-1} =\frac{8}{4} =2$

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