Determine the equation of a line through the point (3,-4) that is perpendicular to the line y=3x+7
1 answer:
Answer:
y = - x - 3
Step-by-step explanation:
The equation of a line in slope- intercept fprm is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 7 is in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
, thus
y = - x + c ← is the partial equation of the perpendicular line
To find c substitute (3, - 4) into the partial equation
- 4 = - 1 + c ⇒ c = - 4 + 1 = - 3
y = - x - 3 ← equation of perpendicular line
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Answer:
1:
2:
3:
Step-by-step explanation:
Question 1: When lines are parallel, that means they're slope is the same and there y-intercept is different. So the first step is to calculate the slope of BC. If you look at BC you'll notice it goes down by 2 and goes forward by 2 so the slope is -2/2 or -1. This completes one part of the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept. The y-intercept will be calculated using the point A. since the equation passes through point A
-1 = (-2)(-1) + b
-1 = 2 + b
-3 = b
y=-1x-3
Question 2: Same concept here, if you look at AC, you'll see it "rises" by 4 and "runs" by 5, thus the slope is 4/5. Since it passes through B we'll use that to find the y-intercept
5 = (4/5)(1) + b
5 = 4/5 + b
b = 4.2
Question 3: It "rises" by 6 and "runs" by 3, thus the slope is 6/3 which is 2.
Plug in known values
3=(3)(2) + b
3 = 6 + b
-3 = b