Option B:
The equation of a line is [tex]y=\frac{7}{2}x-2[/tex].
Solution:
Given data:
Line passing through the point (4, 12).
y-intercept of the line = –2
The equation of a line in slope-intercept form is
y = mx + c
where m is the slope and c is the y-intercept.
c = –2
Substitute c = –2 in slope-intercept form.
y = mx – 2 – – – – (1)
To find m, substitute (4, 12) in the above equation.
12 = m(4) – 2
12 = 4m – 2
Add 2 on both sides of the equation.
14 = 4m
Divide by 2 on both sides of the equation.
[tex]$\frac{14}{4}=m[/tex]
[tex]$\frac{7}{2}=m[/tex]
Slope = [tex]\frac{7}{2}[/tex]
Substitute m value in equation (1), we get
[tex]$y=\frac{7}{2}x-2[/tex]
The equation of a line is [tex]y=\frac{7}{2}x-2[/tex].
Hence Option B is the correct answer.
