Question

A student analyzed the table below and stated the following, “the y-intercept is 4 because (4,0) has a y value of 0”. Is the student correct? Why or why not?

Answer 1

Answer:

No

Why he is not correct is because the y-intercept is the coordinate of the point where the graph meets or crosses the y-axis, which is equivalent to a point on the graph where the x-coordinate value reduces to zero, or to put it in a mathematical form x = 0

Step-by-step explanation:

From the given data, we have;

x     ${}$       y

2     ${}$      -2

4     ${}$       0

6      ${}$      2

8      ${}$      6

The given data is linear because it has a constant first (common) difference of 2

The general form of the straight line equation is y = m·x + c

Where;

m = The slope

c = The y-intercept

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of the graph of the data from any two points, (x₁, y₁) = (4, 0) and (x₂, y₂) = (4, 0)) is m = (2 - 0)/(6 - 4) = 1

The equation representing the data in point and slope form is therefore;

y - 4 = 1 × (x - 0)

Which gives;

y = x + 4

Therefore, the y-intercept = 4.