Please let me know if I figured this out correctly.
Directions:Write an equation for the line that is perpendicular to the given line and that passes through the given point.
1) y=x-3; (4,6) Answer: y=-x-10
Thank you!
no, (4,6) does not satisfy your new equation.
The new equation has to be
y = -x + b, but (4,6) lies on it, so
6 = -4 + b
b = 10
new equation is
y = -x + 10
Thank you!
To find the equation of a line that is perpendicular to the given line (y = x - 3) and passes through a given point (4, 6), you can follow these steps:
Step 1: Determine the slope of the given line.
The given line has a slope of 1 since its equation is in the form y = mx + b, where m represents the slope.
Step 2: Determine the slope of the line perpendicular to the given line.
For two lines to be perpendicular, their slopes must be negative reciprocals of each other. In this case, the perpendicular line's slope will be -1 (negative reciprocal of 1).
Step 3: Use the slope-intercept form of a line (y = mx + b) and substitute the given point's coordinates to find the y-intercept (b).
You are given the point (4, 6), so substitute the x and y values in the equation y = mx + b:
6 = -1(4) + b
6 = -4 + b
b = 10
Step 4: Write the equation for the line.
Now that you have the slope (-1) and the y-intercept (10), substitute these values into the slope-intercept form:
y = -x + 10
Therefore, the equation for the line that is perpendicular to y = x - 3 and passes through the point (4, 6) is y = -x + 10.