Answer:
The graph of the equation is also attached.
From the graph, it is clear that at x = 0, the value of y = 0
Hence, the line passes through the origin with the y-intercept 0.
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given that the profit y (in dollars) for a business from selling x coats is represented by the equation
comparing with the slope-intercept form of the line equation
m = 56
<u>Determining the y-intercept</u>
We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
substitute x = 0 in the equation
y = 56(0)
y = 0
Thus, the y-intercept b = 1
Thus,
The equation y = 5x has:
The graph of the equation is also attached.
From the graph, it is clear that at x = 0, the value of y = 0
Hence, the line passes through the origin with the y-intercept 0.
Let x be the number of days.
Daily pass:
65x + 30x
95x
Season pass:
400 + 30x
95x > 400 + 30x
65x > 400
x > 6.15
The number of days can't be 6.15, so you must round. You can't go down because then the price will be more expensive, so you have to round up.
It would take 7 days until the season pass is less expensive than the daily pass.
----------------------
You can check this by plugging in the x.
95x > 400 + 30x
95(7) > 400 + 30(7)
665 > 400 + 210
665 > 600
The daily pass is more expensive than the season pass.
Each transformation will give these following coordinates
Translation 7 units right gives E(4, 4), F(8, 3), G(10, 6), and H(8, 6) as shown in brown in the diagram below
Reflection on the y-axis gives E(3, 4), F(-1, 3), G(-3, 6) and H(-1, 6) as shown in green in the diagram below
Reflection on the x-axis gives E(-3, -4), F(1, -3), G(3, -6) and H(1, -6) as shown in red in the diagram below
Translation 5 units down gives E(-3, -1), F(1, -2, G(3, 1) and H(1, 1) as shown in purple in the diagram below
<h2>
Answer:</h2>
y = 
x + 3
<h2>
Step-by-step explanation:</h2>
As shown in the graph, the line is a straight line. Therefore, the general equation of a straight line can be employed to derive the equation of the line.
The general equation of a straight line is given by:
y = mx + c <em>or </em>-------------(i)
y - y₁ = m(x - x₁) -----------------(ii)
Where;
y₁ is the value of a point on the y-axis
x₁ is the value of the same point on the x-axis
m is the slope of the line
c is the y-intercept of the line.
Equation (i) is the slope-intercept form of a line
Steps:
(i) Pick any two points (x₁, y₁) and (x₂, y₂) on the line.
In this case, let;
(x₁, y₁) = (0, 3)
(x₂, y₂) = (4, -2)
(ii) With the chosen points, calculate the slope <em>m</em> given by;
m = 
m = 
m =
(iii) Substitute the first point (x₁, y₁) = (0, 3) and m = into equation (ii) as follows;
y - 3 = (x - 0)
(iv) Solve for y from (iii)
y - 3 = x
y = x + 3 [This is the slope intercept form of the line]
Where the slope is and the intercept is 3
