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…

Question

asked Nov 23, 2021 181k views

1 Answer

Alex Bender · Answer 1 · 2021-11-27T03:55:28+0000

Answer:

a + b = 2

Step-by-step explanation:

The equations are determined by the definition of line equation:

First line

$1 = (1)/(3)\cdot (9) + b$ (Line equation)

1 = 3 + b

b = -2 (x-Intercept)

The equation of the first line is:

$y = (1)/(3)\cdot x - 2$

Second line

m = ((-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:

$(1)/(3)\cdot x -2 = -x +2$

$(4)/(3)\cdot x = 4$

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