Question

In the same graph, what is the approximate y-value of the point of the intercetion?
The photo:
A solid line passes through the points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 2 comma 8 right-parenthesis. The region above the line is shaded red. A dotted line passes through the points left-parenthesis 0 comma 2 right-parenthesis and left-parenthesis 2 comma 0 right-parenthesis. The region below the line is shaded blue. A region of the coordinate plane is shaded both red and blue.

A: -1
B: 4
C: 3
D: 2

Answer 1

The solid line passes through the points (0,4) and (2,8), and the dotted line passes through the points (0,2) and (2,0).

When two lines intersect, the y-coordinate of the point of intersection will be the same for both lines.

For the solid line, the y-coordinate at x=0 is 4, and at x=2 is 8. Since the line is linear, we can determine the equation of the line using the slope-intercept form, y = mx + b.

The slope (m) can be calculated as (change in y)/(change in x) = (8-4)/(2-0) = 4/2 = 2.

Substituting one point and the slope into the equation, we have 4 = 2(0) + b, which gives us b = 4.

So, the equation for the solid line is y = 2x + 4.

For the dotted line, the y-coordinate at x=0 is 2, and at x=2 is 0. Again, using the slope-intercept form, we have 2 = m(0) + b, which gives us b = 2.

So, the equation for the dotted line is y = -x + 2.

To find the point of intersection, we can set the two equations equal to each other and solve for x:

2x + 4 = -x + 2

Adding x and subtracting 2 from both sides, we have 3x = -2

Dividing both sides by 3, we get x = -2/3.

To find the y-coordinate, we can substitute this value of x into either equation. Using the equation for the solid line, we have:

y = 2(-2/3) + 4 = -4/3 + 4 = 8/3.

So, the approximate y-value of the point of intersection is 8/3.

Therefore, the answer is not listed among the provided options.