Step-by-step explanation:
<u>Statement Reason </u>
∠5 and ∠7 are vertical angles Vertical angles theorem
m∠5 = m∠7 Definition of vertical angles
m∠5 = -2(3x - 4), m∠7 = 3(x - 3) - 1 Given
-2(3x - 4) = 3(x - 3) - 1 Substitution property of equality
-6x + 8 = 3x - 9 - 1 Distributive property
3x + 6x = 8 + 10 Addition property
9x = 18 Addition property
x = 18/9 Division property
x = 2 Proved
Form equation
y = mx + c
y = (rise/run).x + c
y = (11-1 / 3--2)x + c
y = 2x + c
11 = 2(3) + c
Find c (y-intercept)
11 - 6 = c
c = 5
Final equation of line
y = 2x + 5
Substitute given possible x-values in to find y-values
y = 2(1) + 5 = 7 (1,7)
y = 2(2) + 5 = 9 (2,9)
Therefore d is correct
Answer: No, it is not a solution
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Explanation:
The point (3,-4) means that x = 3 and y = -4 pair up together
Let's plug these x,y values into each equation
Starting with the first equation, we get,
y = 4x-16
-4 = 4(3)-16 ... x replaced with 3; y replaced with -4
-4 = 12-16
-4 = -4 .... this is a true statement
Repeat for the second equation
y = 2x-6
-4 = 2(3)-6
-4 = 6-6
-4 = 0 ... this is false
Since we get a false statement, this means (3,-4) is not on the line y = 2x-6, which means that overall (3,-4) is not a solution to the system of equations. The point (3,-4) must make both equations true for it to be a solution.
Answer:
4) y = 9
5) x = -1
6) y = -5x − 9
Step-by-step explanation:
4) x = 3 is a vertical line with an x-intercept of (3, 0). It has an undefined slope.
A perpendicular line to that will be y = a, which is a horizontal line with a y-intercept of (0, a) and a slope of 0. Since this line passes through (3, 9), the equation of the line must be y = 9.
5) The y-axis is x = 0. A parallel line that includes the point (-1, -2) is x = -1.
6) Parallel lines have the same slope, so:
y = -5x + b
To find the value of b (the y-intercept), plug in the point (-2, 1):
1 = -5(-2) + b
1 = 10 + b
b = -9
y = -5x − 9
