Question

write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation. a. f(x) = 2x 12 b.f(x) = 6x − 12 c. y = 2x 12 d.y = 6x − 12

Answer 1

The slope-intercept form: $y= mx + b$

The slope-point form: $y-y_1=m(x-x_1)$

The slope: $m=\dfrac{y_2-y_1}{x_2-x_1}$

$(3; 6)\to x_1=3;\ y_1=6\\(5;\ 18)\to x_2=5;\ y_2=18$

subtitute

$m=\dfrac{18-6}{5-3}=\dfrac{12}{2}=6$

$y-6=6(x-3)\\\\y-6=6x-18\ \ \ \ |add\ 6\ to\ both\ sides\\\\y=6x-12$

Answer: b. f(x)=6x - 12