Question

The table of ordered pairs shows the coordinates of the two points on the graph of a line. Which equation describes the line?

a. Y = x + 7
b. Y = x - 7
c. Y = -5x + 2
d. Y = 5x + 2

Please select the best answer from the choices provided. ​

Answer 1

Explanation:

To determine the equation of the line, we need to find the slope of the line passing through the two given points.

Let the coordinates of the two points be (x1, y1) and (x2, y2). Then the slope of the line passing through these points is:

slope = (y2 - y1) / (x2 - x1)

From the table of ordered pairs, we can see that the two points are (0, 2) and (1, 7). So, x1 = 0, y1 = 2, x2 = 1, and y2 = 7.

Therefore, the slope of the line passing through these points is:

slope = (7 - 2) / (1 - 0) = 5

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the points on the line.

Using the point (0, 2), we have:

y - 2 = 5(x - 0)

Simplifying this equation gives:

y = 5x + 2

Comparing this equation with the given choices, we see that the correct answer is d.

Therefore, the equation of the line passing through the two points is Y = 5x + 2.