Question

(b) what is the coordinates of the point where the two lines intersect?

Explanation:

Step1: Analyze the graph

We need to find the point where the two lines (the one passing through A and B, and the one passing through C and D) intersect. By looking at the grid, we can estimate the coordinates by finding the common point of the two lines.

Step2: Identify the intersection point

From the graph, we can see that the two lines intersect at a point. Let's check the x and y coordinates. By observing the grid lines, the x - coordinate seems to be 4 (since it's 4 units to the right of the origin on the x - axis) and the y - coordinate seems to be - 1 (since it's 1 unit below the origin on the y - axis). Wait, maybe a better way: let's find the equations of the lines.

First, for the line through A(0, - 3) and B(9, 0):
The slope $m_1=\frac{0 - (-3)}{9 - 0}=\frac{3}{9}=\frac{1}{3}$. Using the slope - intercept form $y = mx + b$, with $b=-3$ (since it passes through (0, - 3)), the equation is $y=\frac{1}{3}x-3$.

For the line through C(0, 1) and D(1, 0):
The slope $m_2=\frac{0 - 1}{1 - 0}=- 1$. Using the slope - intercept form $y=mx + b$, with $b = 1$ (since it passes through (0,1)), the equation is $y=-x + 1$.

To find the intersection, set the two equations equal:
$\frac{1}{3}x-3=-x + 1$
$\frac{1}{3}x+x=1 + 3$
$\frac{1 + 3}{3}x=4$
$\frac{4}{3}x=4$
$x = 3$

Substitute $x = 3$ into $y=-x + 1$: $y=-3 + 1=-2$

Wait, maybe my initial visual estimate was wrong. Let's re - check the graph. The two lines: the line from A(0, - 3) to B(9, 0) and the line from C(0,1) to D(1,0). Let's find the intersection by solving the system.

Equation 1: $y=\frac{1}{3}x-3$

Equation 2: $y=-x + 1$

Set $\frac{1}{3}x-3=-x + 1$

Multiply both sides by 3 to eliminate the fraction:

$x-9=-3x + 3$

$x + 3x=3 + 9$

$4x=12$

$x = 3$

Then $y=-3 + 1=-2$

So the intersection point is (3, - 2)

Wait, maybe I made a mistake in the first visual check. Let's look at the graph again. The line from A(0, - 3) goes up to B(9,0), and the line from C(0,1) goes down to D(1,0). The intersection should be at x = 3, y=-2. Let's confirm with the grid. At x = 3, moving up from the x - axis, y=-2. Yes, that makes sense.

Answer:

(3, - 2)