Question

determine the equation of the line that passes through the given points. (if you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)
(10, 2) and (-3, 2)
a. \\( y = 2x \\)
b. \\( y = 2x - 3 \\)
c. \\( y = 2 \\)
d. \\( y = 2x + 10 \\)

please select the best answer from the choices provided

\\( \circ \\) a
\\( \circ \\) b
\\( \circ \\) c
\\( \circ \\) d

Explanation:

Step1: Analyze the y - coordinates of the points

The two given points are \((10, 2)\) and \((- 3,2)\). We can see that the \(y\) - coordinate for both points is \(2\).

Step2: Recall the equation of a horizontal line

A horizontal line has the equation of the form \(y = k\), where \(k\) is the constant \(y\) - coordinate of all the points on the line. Since the \(y\) - coordinate of both given points is \(2\), the equation of the line passing through these two points is \(y=2\). We can also check by substituting the points into the other equations:

• For option a: If \(x = 10\), \(y=2\times10 = 20

eq2\), so option a is incorrect.

• For option b: If \(x = 10\), \(y=2\times10-3=17

eq2\), so option b is incorrect.

• For option d: If \(x = 10\), \(y=2\times10 + 10=30

eq2\), so option d is incorrect.

Answer:

C. \(y = 2\)