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Answer:
B, C
Step-by-step explanation:
The equation of a line can be given by y -y₁= m(x -x₁), where m is the slope. This is also known as the point-slope form.
Slope of the line
= -4
<em>Substitute m= -4 into the equation:</em>
y -y₁= -4(x -x₁)
<em>Substitute a pair of coordinates into (x₁, y₁):</em>
Let's start by substituting (1, 2).
y -2= -4(x -1)
This gives us the same equation as D, making D an incorrect option. Note that the question asks for which is not the correct equation.
Let's change the above into the slope-intercept form, where by y is the subject of formula.
<em>Start by expanding the right-hand side:</em>
y -2= -4x +1
<em>+</em><em>2</em><em> on both sides:</em>
y= -4x +3
This equation is not the same as C. C is thus the correct option.
Let's check for options A and B.
The equation in option B is not the correct equation either as they have substituted (2, 1) instead of (1, 2) into (x₁, y₁). Thus, option B is also correct.
y -y₁= -4(x -x₁)
Substitute (3, -6) into (x₁, y₁):
y -(-6)= -4(x -3)
y +6= -4(x -3)
This is the same as option A, making option A incorrect too.
Answer:
Step-by-step explanation:
<u>Geometric Sequences</u>
There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.
In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the sequence:
112, -28, 7, ...
It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.
Let's find the common ratio by dividing each term by the previous term:
Testing with the third term:
Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term: