Question

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

(5, 2) and (-1, 2)

Short answer

The equation of the line passing through the point (5, 2) and (-1, 2) is:$y=2$

Step-by-step solution

Step 1. Given information:

Given two points are (5, 2) and (-1, 2).

Step 2. Concepts

Here we can use slope and slope - point formula to find the equation of the line.

Slope =$\frac{y_2-y_1}{x_2-x_1}$

Slope - point formula:

$y-y_2=m(x-x_2)$

Step 3. Explanation

Using slope formula,

$m=\frac{2-2}{-1-5}$

$\Rightarrow m=0$

Using equation of the line,

$y-y_1=m(x-x_1)$

Substituting the slope and one of the given point,

$y-2=0(x-5)$

Multiplying zero by any number or term by zero we get the result is zero.

Therefore equation of the line is y = 2.

So slope intercept form is looks like:

$y=0x+2$

Step 4. Conclusion

Hence, equation of the line passing trough the points (5, 2) and (-1, 2) is$y=0x+2$.