Answer
The equation of line in function notation is:
[tex]f(x)=4x-6[/tex]
Step-by-step explanation:
Given points:
(3,6) and (4,10)
To find the equation of the line in function notation.
Solution:
In order to find the equation of the line we will first find the slope of the line.
The slope of a line passing through points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] the slope can be given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging in the given points to find the slope of the line.
[tex]m=\frac{10-6}{4-3}[/tex]
[tex]m=\frac{4}{1}[/tex]
∴ [tex]m=4[/tex]
Equation of line can be written in point slope form as:
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on the line.
Using point (3,6)
[tex]y-6=4(x-3)[/tex]
Using distribution:
[tex]y-6=4x-12[/tex]
Adding 6 both sides.
[tex]y-6+6=4x-12+6[/tex]
[tex]y=4x-6[/tex] [Equation of line]
To write the equation in function notation, we will replace [tex]y[/tex] with [tex]f(x)[/tex].
So, the equation of the line in function notation can be given as:
[tex]f(x)=4x-6[/tex]
