Question

What is the equation in slope-intercept form of the line that passes through the point (-4,0) and is perpendicular to the line represented by y = -x - 1?

Answer 1

The equation in slope-intercept form of the line that passes through the point (-4,0) and is perpendicular to the line y = -x - 1 is y = x + 4.

Step-by-step explanation:

The equation in slope-intercept form of the line that passes through the point (-4,0) and is perpendicular to the line represented by y = -x - 1 can be found using the following steps:

1. Find the slope of the given line. The given line has a slope of -1.
2. Since the line we are looking for is perpendicular to the given line, the slope of the new line will be the negative reciprocal of -1, which is 1.
3. Use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (-4,0) and m is the slope we found in step 2.
4. Substitute the values into the equation and simplify to get the slope-intercept form.

Therefore, the equation in slope-intercept form of the line that passes through the point (-4,0) and is perpendicular to y = -x - 1 is y = x + 4.