Answer:
Step-by-step explanation:
There is a relationship between lines that are perpendicular. Their slopes are negative reciprocals of each other. Example: if one line has a slope of 4/3 then a line with the slope of -3/4 is perpendicular to it (they intersect at right angles).
So to find the slope of a line perpendicular to y = -2/3x + 4 we must know the slope of it. The slope, when the line is in the slope-intercept form (aka y = mx + b), is the multiplier in front of the "x" so in this case it is -2/3. So a line perpendicular to it has a slope of 3/2.
Now that we know the slope (m = 3/2) we can find the equation of the line that has a slope of 3/2 but goes through the point (-2, -2) in a couple of ways.
1) Use the slope-intercept form of a line and plug in the values of x = -2 and y = -2 (from the point (-2, -2) like this:
y = mx + b
y = 3/2x + b
-2 = 3/2(-2) + b
-2 = -3 + b
1 = b
So y = 3/2x + 1
2) We can use the point-slope equation y - y1 = m(x - x1) which works great if you know the value of m (we do, m = 3/2) and some point (x1, y1) on the line (and we do, (-2, -2); so x1 = -2 and y1 = -2):
y - y1 = m(x - x1)
y - y1 = 3/2(x - x1)
y - (-2) = 3/2(x - (-2))
y + 2 = 3/2(x + 2)
Although it looks different than the other equation, it is really the same. Just distribute and combine like-terms and you'll see it's the same. So either is an acceptable answer for this quest
<span>B) y = -3x3
</span>-----------------------------------
Answer:
Segment BF = 16
Step-by-step explanation:
The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately
The given theorem is the Triangle Proportionality Theorem
According to the theorem, given that segment DE is parallel to segment BC, we have;
Therefore;
Which gives;
Similarly, given that EF is parallel to AB, we get;
Therefore;
Which gives;
Therefore, the statement that can be proved using the given theorem is segment BF = 16.
First, you need to have j on it own. Since j is over 4-8, you times both sides of the inequality so the /4-8 is canceled.
Your new inequality equation is j<4(4-8). Solve the bracket and then times the answer by 4.
~ j<4(-4)
~ j<-16
Answer:
5/8
Step-by-step explanation:
To find the slope, use the formula
m = (y2-y1)/(x2-x1)
= (2 - -3)/(6 - -2)
= (2+3)/(6+2)
= 5/8