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 [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] then,
the general form of the equation of line is given by;
[tex]y-y_1=m(x-x_1)[/tex]; where m is the slope given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Consider the given points;
(1, 7) and (5 , 15)
First calculate the slope (m);
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{15-7}{5-1} =\frac{8}{4} =2[/tex]
Therefore, slope of the line, m=2
Then, the equation of line is:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the value of m=2 and (1, 7) above we get;
[tex]y-7=2(x-1)[/tex]
or
[tex]y-7=2x-2[/tex]
Add 7 to both sides of an equation we get;
[tex]y-7+7=2x-2+7[/tex]
Simplify:
[tex]y=2x+5[/tex]
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
