Does (8,4) make the equation y = x true?
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The equation of the parallel line in slope-intercept form is;
y = x -
Step-by-step explanation:
Let us revise some facts about parallel lines
The equations of two parallel lines have:
- Same slopes
- Different y-intercept
The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept
The given line has equation 5x - 2y = 10
Put it in the form of y = m x + b to find its slope
∵ 5x - 2y = 10
- Subtract 5x from both sides
∴ -2y = 10 - 5x
- Divide to sides by -2
∴ y = -5 + x
∴ y = x - 5
- The value of m is the coefficient of x
∴ m =
∴ The slope of the given line is
∵ Parallel lines have same slopes
∴ The slope of the parallel line is m =
- Substitute the value of m in the form of the equation
∴ The equation of the parallel line is y = x + b
To find b substitute x and y in the equation by the coordinates of any point lies on the line
∵ The parallel line passes through point (3 , -5)
- Substitute x and y by the coordinates of the point (3 , -5)
∵ x = 3 and y = -5
∴ -5 = (3) + b
∴ -5 = + b
- Subtract from both sides
∴ b =
∴ The equation of the parallel line is y = x +
∴ The equation of the parallel line is y = x -
The equation of the parallel line in slope-intercept form is;
y = x -
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/8628615
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Answer:
Part A)
1) The graph in the attached figure N 1
2) The coordinate rule is (x,y) -----> (x,y+10)
3) The translation of the function up 10 units means that the initial deposit is $60 instead of $50
Part B)
1) The graph in the attached figure N2
2) The coordinate rule is (x,y) -----> (x-10,y)
3) The translation of the function right 10 units means that the initial deposit is equal to $10
Part C)
1) In each translation, the slope is the same (m=5) are parallel lines
2) The vertical translation would be up 40 units
Step-by-step explanation:
we have
where
f(x) --> represents Jeremy's account balance
x ---> the time in years
Part A)
The translation of the function is up 10 units.
The rule of the translation is equal to
(x,y) -----> (x,y+10)
so
The new function will be
The graph in the attached figure N 1
The translation of the function up 10 units means that the initial deposit is $60 instead of $50
Part B)
The translation of the function is right 10 units.
The rule of the translation is equal to
(x,y) -----> (x-10,y)
so
we have
----> function Part A
The new function will be
The graph in the attached figure N 2
The translation of the function right 10 units means that the initial deposit is equal to $10
Part C)
1. Look at the translations, what characteristic of the graph stayed the same in each translation?
In each translation, the slope is the same
The slope m is equal to m=5
Are parallel lines
2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position?
we have
The vertical translation would be up 40 units
The rule of the translation is equal to
(x,y) -----> (x,y+40)
so
The new function will be
