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
