Question

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line y = −5, point (−4, 3)

Short answer

The line parallel to y = -5 passing though the point (-4, 3) is y = 3.

Step-by-step solution

Step 1. Given information

Given equation of the the line is x = -5

and the given point is (-4, 3).

Step 2.  Concept

We can first write original equation in the y = mx + b form and compare to find the lope of the given equation.

Slope of two parallel lines is same.

Then we will use slope - point formula to find the equation of parallel line.

Step 3. Explanation

We have given equation of line is y = - 5.

Rewriting it in the slope - intercept form,

y = 0x - 5.

Comparing it with y = mx + b we get slope of the given line is 0.

Now using slope - point formula,

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

Substituting the point and slope,

$y-3=0(x+4)$

Simplifying,

y = 3

Step 4. Conclusion

Hence, equation of parallel line to y = -5 passing through the point (-4, 3) is y = 3.