Answer:
Options B and E are correct.
Step-by-step explanation:
Let the equation of the given line is y = mx + c
This line passes through two points (1, 13) and (-2, 4)
So slope of the line m = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{13-4}{1+2}=\frac{9}{3}=3[/tex]
y-intercept of the line is 10
Therefore equation will be y = 3x + 10
Now we take the options one by one.
A. y - 2 = 3(x - 4)
y = 2 + 3x - 12
y = 3x - 10
Option is incorrect because the given line in this option doesn't matches with the equation of the line.
B. y - 4 = 3(x + 2)
y = 4 + 3x + 6
y = 3x + 10
Correct option.
C. y - 1 = 3(x - 13)
y = 1 + 3x - 39
y = 3x - 38
Incorrect option.
D. y - 4 = 3( x- 2 )
y = 4 + 3x - 6
y = 3x - 2
Incorrect option
E. y - 13 = 3(x - 1)
y = 13 + 3x -3
y = 3x + 10
Correct option.
F. y + 2 = 3(x - 4)
y = -2 + 3x - 12
y = 3x - 14
Incorrect option.
Therefore, Options B and E are the correct options.
