Question

the graph of a line in the xy-plane slope 1/3 and contains the point (9,1). the graph of a second line passes through the points (-2,4) and (5,-3). if the two lines intersect at (a,b), what is the value of a+b?

Answer 1

Answer:

$a + b = 2$

Explanation:

The equations are determined by the definition of line equation:

First line

$1 = \frac{1}{3}\cdot (9) + b$ (Line equation)

$1 = 3 + b$

$b = -2$ (x-Intercept)

The equation of the first line is:

$y = \frac{1}{3}\cdot x - 2$

Second line

$m = \frac{(-3)-4}{5-(-2)}$

$m = - 1$ (Slope)

$-3 = -1 \cdot (5)+b$

$-3 = -5 + b$

$b = 2$ (x-Intercept)

The equation of the second line is:

$y = -x + 2$

First, y is eliminated by equalization and x is found:

$\frac{1}{3}\cdot x -2 = -x +2$

$\frac{4}{3}\cdot x = 4$

$x = 3$ (a)

Now, y is finally determined by direct substitution:

$y = -3+2$

$y = -1$ (b)

The value of a + b is:

$a + b = 2$