Question

If ay=x+b is the equation of the line passing through the points (-5,-2) and (4, 7), then the value of 2a + b is equal to

• A. 1
• B. 3
• C. 5
• D. -3
• E. -1

Answer 1

The Correct Option is C

Given equation of the line: 

\( ay = x + b \)

Rewriting in standard form:

\( y = \frac{1}{a} x + \frac{b}{a} \)

Finding the slope of the line passing through points (-5, -2) and (4, 7):

\(\text{Slope} = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - (-2)}{4 - (-5)} = \frac{7 + 2}{4 + 5} = \frac{9}{9} = 1\)

Comparing with the equation \( y = mx + c \), we get:

\(\frac{1}{a} = 1 \Rightarrow a = 1\)

Substituting one point (-5, -2) into \( y = x + \frac{b}{a} \):

\(-2 = (-5) + \frac{b}{1}\)

\(-2 = -5 + b\)

\(b = 3\)

Calculating \( 2a + b \):

\(2(1) + 3 = 2 + 3 = 5\)

Thus, the correct answer is:

5