Write an equation of a line perpendicular to line AB below in slope-intercept form that passes through the point (7, 6).
A (0,1)
B (-2,5)
y - 6 = .5x - 3.5
y = .5x - 3.6 + 6
y = .5x + 2.5
So I continued working where you left off and got y=0.5x+2.5 is that correct? or is it y=0.5x-2.5? I am pretty sure that it is the first one but I just wanna make sure.
To find the equation of the line perpendicular to line AB, we need to determine the slope of line AB and then find the negative reciprocal of that slope.
Step 1: Find the slope of line AB.
The formula to find the slope (m) of a line given two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates of points A (0,1) and B (-2,5), we can find the slope of line AB:
m = (5 - 1) / (-2 - 0)
m = 4 / -2
m = -2
So the slope of line AB is -2.
Step 2: Find the negative reciprocal of the slope.
The negative reciprocal of a slope is simply the negative value of its reciprocal.
Reciprocal of -2 = -1/2
Negative of -1/2 = 1/2
So, the slope of the line perpendicular to AB is 1/2.
Step 3: Use the slope-intercept form of a linear equation to write the equation of the line.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Since the line passes through the point (7, 6), we can substitute these values into the equation and solve for b:
6 = (1/2)(7) + b
6 = 7/2 + b
Simplify and isolate b:
6 - 7/2 = b
12/2 - 7/2 = b
5/2 = b
So, the y-intercept b is 5/2.
Finally, we can write the equation of the line perpendicular to AB in slope-intercept form:
y = (1/2)x + 5/2
slope of AB = 4/-2 = -2
so slope of new line = +1/2
new line:
y-6 = (1/2)(x-7)
expand and doctor it up any way you want.