Respuesta :
The slope = (10-6) / (4-3) = 4
using the general equation y - y1 = m(x - x1) where m = slope and (x1,y1) is a point on the line, we have:-
y - 6 = 4(x - 3)
y = 4x - 12 + 6
y = 4x - 6 (answer)
The correct answer is option A. f(x) = 4x - 6.
Equation of the line
Given:
The line passes through the points (3, 6) and (4, 10).
To find:
the equation of the line that passes through the points (3, 6) and (4, 10) utilizing the function notation.
Let, [tex](x_{1}, y_{1} )[/tex] = (3,6) and [tex](x_{2}, y_{2} )[/tex] =(4,10)
[tex]$m=(y 2-y 1) /(x 2-x 1)[/tex]
[tex]$=(10-6) /(4-3)[/tex]
[tex]=4 / 1[/tex]
[tex]=4[/tex]
Where, equation of the line
y = mx + b
y = 4x + b
Consider any one of the points (x, y) = (3, 6) or (x, y) = (4, 10).
Take, (x, y) = (3, 6)
y = mx + b
Substituting the values of x and y
[tex]$6=4 * 3+b$[/tex]
Simplifying the equation as
[tex]$6-12=b[/tex]
[tex]$b=-6[/tex]
The equation of line, y = mx + b
y = 4x - 6
Therefore, the correct answer is option A. f(x) = 4x - 6.
To learn more about the equation of the line
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