Find the slope of the line between (-7,-2) and (9,4)A)-3/8
B)3/8
C)6/17
D)2/5
———————————-
Find the slope of the line between (5,-6) and (-1,8)
A)-7/3
B)-3/7
C)-14/5
D)-13/6
—————————————
Find the slope of the line
Y=1/8x-1
A)-8/1
B)1/8
C)1
D)-1
——————————————
Find the y-intercept of the following equation
Y=7/2x-10/7
A)7/2
B)-7/2
C)10/7
D)-10/7
Plz help my I don’t get it
Worth 18 points thx
I’m really struggling plz help
Answers
B, A, B, D
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 7, - 2) and (x₂, y₂ ) = (9, 4)
m = =
=
repeat with (x₁, y₁ ) = (5, - 6) and (x₂, y₂) = (- 1, 8)
m = =
= -
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = x - 1 is in this form
with slope m =
To find the y- intercept , let x = 0, in the equation
x = 0 : y = 0 - = -
← y- intercept
Final answer:
The slopes of the lines between the given pairs of points are 3/8 and -7/3 respectively. The slope of the line Y = 1 / 8x - 1 is 1 / 8 and the y-intercept of the equation Y = 7 / 2x - 10 / 7 is -10 / 7.
Explanation:
The slope between two points is found by using the formula m = (y2 - y1) / (x2 - x1). Let's calculate for the first two. For (-7, -2) and (9, 4), the slope m = (4 - (-2)) / (9 - (-7)) = 6 / 16 =
3 / 8
. So, the correct answer is B. For the second pair of points (5, -6) and (-1, 8), m = (8 - (-6)) / (-1 - 5) = 14 / -6 = -
7 / 3
. So, the answer is A. The slope of the line of an equation in the form of y = mx + b is the coefficient of x (m), so for the line Y = 1 / 8x - 1, the slope is
1 / 8
. The answer is B. The y-intercept (b) is the constant term in the equation y = mx + b, so for the equation y = 7 / 2x - 10 / 7, the y-intercept is -
10 / 7
. The answer is D.
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Step-by-step explanation:
Part 1: Find GCF of variables
The equation gives d ² and d as variables. The GCF rules for variables are:
- The variables must have the same base.
- If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.
- If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.
The GCF for the variables is d.
Part 2: Find GCF of bases (Method #1)
The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.
Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!
Prime Factorization of 108
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.
Prime Factorization of 216
216 ⇒ 108 & 2
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.
After completing the prime factorization trees, check for the common factors in between the two values.
The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.
Therefore, the greatest common factor (combining both the coefficient and the variable) is .
Part 3: Find GCF of bases (Method #2)
This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.
Therefore, the coefficient of the GCF will be 108.
Then, follow the process described for variables to determine that the GCF of the variables is d.
Therefore, the GCF is .
Answer:
Below
Step-by-step explanation:
If d is a positive number then the greatest common factor is 108d.
To get it isolate d and d^2 from the numbers.
108 divides 216. (216 = 2×108)
Then the greatest common factor of 216 and 108 is 108.
For d^2 and d we will follow the same strategy
d divides d^2 (d^2 = d*d)
Then the greatest common factor of them is d.
So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer