Answer:
Value of k = -2
Step-by-step explanation:
Using slope intercept form:
The equation of line is given by:
y = mx+b
where, m is the slope and b is the y-intercept.
As per the statement:
The graphs of y = f(x) and y = g(x) are shown on the coordinate plane.
First find f(x):
Consider two points on y=f(x) are:
(0,-3) and (2, 1)
Formula for slope:
then;
then;
Substitute the point (0, -3) to solve for b:
⇒
∴ 
Similarly for g(x):
Consider two points on y = g(x) are:
(0, 6) and (2, -2)
then;
then;
then;
Substitute the points (0, 6) to solve for b:
⇒
then we get an equation:
y = g(x) = -4x+6
It is given that: If g(x) = k* f(x)
Solve for k:
⇒
on comparing both sides we have;
⇒
Divide both sides by -2 we have;
or
-3k = 6
⇒k = -2
Therefore, the value of k is, -2
Answer:
Y= 5/3x + -9
Step-by-step explanation:
Well its
y=mx+b
m is slope
B is y intercept
To fidn y intercept, just make sure the X value of any coordiante given is 0 and the y value is not 0. So basically anything with (0, y), thats your y intercept.
Slope Is just
(y2-y1) / (x2-x1)
You have to say how diagrams and equations help to figure out ratio and rate problems, you have to figure it on your own, there really isnt an exact answer
Answer:
yes
Step-by-step explanation:
the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.
the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).
so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.
but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.
there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).
but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.
Answer:
3 to the powered of 7
Step-by-step explanation:
