Which equation represents the line that passes through the points (1, 1) and
(-4, 7)?
A. 5x + 6y = 11
B. 6x + 5y = 11
C. 6x - 5y = -11
D. 5x - y = -11


PLEASE HELP

ILL GIVE YOU BRAINIEST

Answer:

Option (B)

Step-by-step explanation:

Let the equation of the line is,

y = mx + b

Here m = slope of the line

b = y-intercept

Slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of the line which passes through the points (1, 1) and (-4, 7) will be,

m = [tex]\frac{7-1}{-4-1}[/tex]

   = [tex]-\frac{6}{5}[/tex]

By substituting the value of m in the equation,

y = [tex]-\frac{6}{5}x+b[/tex]

Since, this line passes through (1, 1),

1 = [tex]-\frac{6}{5}(1)+b[/tex]

b = [tex]1+\frac{6}{5}[/tex]

  = [tex]\frac{11}{5}[/tex]

Therefore, equation will be,

[tex]y=-\frac{6}{5}x+\frac{11}{5}[/tex]

5y = -6x + 11

6x + 5y = 11

Option B is the answer.

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