Answer:
y = 4/3x - 4
Step-by-step explanation:
to find the equation of a line with 2 points, we use the slope formula which is:
we will use (6,4) as ![x_1[tex] and [tex]y_1](https://tex.z-dn.net/?f=x_1%5Btex%5D%20and%20%5Btex%5Dy_1)
and we will use (-3,-8) as ![x_2[tex] and [tex]y_2](https://tex.z-dn.net/?f=x_2%5Btex%5D%20and%20%5Btex%5Dy_2)
. we plug this into the slope formula:
-8 - 4 = -12
-3 - 6 = -9
the slope is 
but we can simplify this further by dividing the fraction by -3
-12 / -3 = 4
-9 / -3 = 3
the simplified version of the slope is 
we can write this in slope-intercept form which is y =mx + b, with b being the y intercept and m being the slope
y = 4/3x + b <--- we need to solve for <em>b</em> in order to find the y intercept, so substitute x & y for a point on the line, we can use any point we are given, but for this example i will use (6,4)
4 = 4/3(6) + b < multiply 4/3 x 6
4 = 8 + b < subtract 8 from both sides
-4 = b
our y intercept would be (0,-4)
the equation looks like the following:
y = 4/3x - 4, which is our answer
Answer:
<em>Part A </em>C = (10,5)<em> Part B </em>C. D'(0,10)
Step-by-step explanation:
<em>Part A</em>
Since c is at the point (2,1) in relation to the origin, we can multiply those distances by our scale factor of 5
(2,1) * 5 = (10,5)
The new point C is going to be (10,5)
<em>Part B</em>
If you dilate with a factor of 5 -- relative to the origin -- you have to multiply the distance from <em>the origin</em> by 5.
In this case, point D is already on the y axis, so it's x value wouldn't be affected. Point D is currently 2 units away from (0,0), so we can multiply 2*5 to get 10 -- our ending point is (0,10)
Answer: A
Step-by-step explanation:
The sum to infinity of a geometric series is
S (∞ ) = \frac{a}{1-r} ( - 1 < r < 1 )
where a is the first term 8 and r is the common ratio, hence
S(∞ ) = {8}{1-\{1}{2} } = {8}{1}{2} } = 16
Answer:
-3
Step-by-step explanation:
Simplifying
4(4m + -3) + -1(m + -5) = -52
Reorder the terms:
4(-3 + 4m) + -1(m + -5) = -52
(-3 * 4 + 4m * 4) + -1(m + -5) = -52
(-12 + 16m) + -1(m + -5) = -52
Reorder the terms:
-12 + 16m + -1(-5 + m) = -52
-12 + 16m + (-5 * -1 + m * -1) = -52
-12 + 16m + (5 + -1m) = -52
Reorder the terms:
-12 + 5 + 16m + -1m = -52
Combine like terms: -12 + 5 = -7
-7 + 16m + -1m = -52
Combine like terms: 16m + -1m = 15m
-7 + 15m = -52
Solving
-7 + 15m = -52
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '7' to each side of the equation.
-7 + 7 + 15m = -52 + 7
Combine like terms: -7 + 7 = 0
0 + 15m = -52 + 7
15m = -52 + 7
Combine like terms: -52 + 7 = -45
15m = -45
Divide each side by '15'.
m = -3
Simplifying
m = -3
Hope this helped :)
