write an equation in point-point form for the line through the given point with the givedescribe how the graph of y | x| -4 is l
ike the graph of y= |x| and how it is different. slope. (-3,-7); m=-6/5
1 answer:
a) The point-slope form of the equation of a line through point (h, k) with slope m is
y - k = m(x - h)
In point-slope form, the equation of the line through (-3, -7) with slope -6/5 is
y + 7 = (-6/5)(x + 3)
b) The graph of
y = |x|-4
represents a translation downward 4 units of the graph of
y = |x|
It retains the same general shape and axis of symmetry, but will have two (2) x-intercepts instead of one (1).
y - k = m(x - h)
In point-slope form, the equation of the line through (-3, -7) with slope -6/5 is
y + 7 = (-6/5)(x + 3)
b) The graph of
y = |x|-4
represents a translation downward 4 units of the graph of
y = |x|
It retains the same general shape and axis of symmetry, but will have two (2) x-intercepts instead of one (1).
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✩ Answer:
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✩ Step-by-step explanation:
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✺ Quadratic polynomials can be factored using the transformation , where
and
are the solutions of the quadratic equation
:
✺ All equations of the form can be solved using the quadratic formula:
✺ The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction:
✺ Take the square root of :
✺ Multiply times
:
✺ Now solve the equation when ± is plus. Add
to
:
✺ Divide by
:
-OR-
✺ Now solve the equation when ± is minus. Subtract
from
:
✺ Divide by
:
✺ Optional : Factor the original expression using . Substitute
for
and
for
:
✩ Answer:
✺ <u>Factored Form</u>:
✺ <u>Exact Form</u>:
✺ <u>Graph Point Form</u>:
"ටᆼට"
Answer:
1) The graph labeled and the ordered pairs plotted are shown in the second picture.
2) To calculate the amount of meat (in pounds) needed for a party of 75 people:
Substitute the value of the Constant of proportionality and into the equation
and then evaluate (The result is 30 pounds).
Step-by-step explanation:
<h3> The missing graph is attached.</h3>Proportional relationships have the following form:
Where "k" is the Constant of proportionality.
1) You can observe in the graph shown in the first picture this point:
So you can subsitute the coordinates of this point into and solve for "k":
Now you can find the amount of meat needed for 20, 30, 40, and 50 people with this procedure:
<u>For 20 people</u>
Substituting and
into the equation
and evaluating, you get:
The ordered pair is:
<u>For 30 people</u>
Substituting and
into the equation
and evaluating, you get:
The ordered pair is:
<u>For 40 people</u>
Substituting and
into the equation
and evaluating, you get:
The ordered pair is:
<u>For 50 people</u>
Substituting and
into the equation
and evaluating, you get:
The ordered pair is:
Knowing those values of "y"and having the ordered pairs, you can finish labeling the graph an plotting the ordered pairs (See the second picture.).
2) Substituting and
into the equation
and evaluating, you can calculate the amount of meat (in pounds) needed for a party of 75 people. This is:
