Write the equation of a line that is perpendicular to the given line and that passes through the given point. y – 3 = (x + 2); (–2, 3)
The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5. The functions have the same shape. The y -intercept of y = | x | is 0, and the y -intercept of the second function is 5. The functions have the same y-intercept. The second function is steeper than y = |x|. The functions have the same y -intercept. The second function is steeper than y = | x |. The two functions are the same. The two functions are the same. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –5. The functions have the same shape. The y -intercept of y = | x | is 0, and the y -intercept of the second function is –5. Skip to navigation
To find the equation of a line that is perpendicular to the given line and passes through the given point, we first need to determine the slope of the given line.
The given line equation is y - 3 = x + 2.
We can rearrange this equation to the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
Add 3 to both sides of the equation:
y = x + 5
From this equation, we can see that the slope of the given line is 1.
The slope of a line perpendicular to a line with slope m is the negative reciprocal of m.
Therefore, the slope of the perpendicular line will be -1.
Next, we can use the point-slope form of a line to find the equation of the perpendicular line.
The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Using the point (-2, 3) and the slope -1, we can write the equation as follows:
y - 3 = -1(x - (-2))
Simplifying the equation further:
y - 3 = -1(x + 2)
y - 3 = -x - 2
y = -x + 1
Therefore, the equation of the line that is perpendicular to y – 3 = (x + 2) and passes through (-2, 3) is y = -x + 1.