Answer:
[tex]a + b = 2[/tex]
Explanation:
The equations are determined by the definition of line equation:
First line
[tex]1 = \frac{1}{3}\cdot (9) + b[/tex] (Line equation)
[tex]1 = 3 + b[/tex]
[tex]b = -2[/tex] (x-Intercept)
The equation of the first line is:
[tex]y = \frac{1}{3}\cdot x - 2[/tex]
Second line
[tex]m = \frac{(-3)-4}{5-(-2)}[/tex]
[tex]m = - 1[/tex] (Slope)
[tex]-3 = -1 \cdot (5)+b[/tex]
[tex]-3 = -5 + b[/tex]
[tex]b = 2[/tex] (x-Intercept)
The equation of the second line is:
[tex]y = -x + 2[/tex]
First, y is eliminated by equalization and x is found:
[tex]\frac{1}{3}\cdot x -2 = -x +2[/tex]
[tex]\frac{4}{3}\cdot x = 4[/tex]
[tex]x = 3[/tex] (a)
Now, y is finally determined by direct substitution:
[tex]y = -3+2[/tex]
[tex]y = -1[/tex] (b)
The value of a + b is:
[tex]a + b = 2[/tex]
