Use the graph to derive the equation y = mx for a line through the origin. simplify the numerical coefficient, if needed.
graph coordinates are, (3,3),(8,8)
answers
y=8x
y=x
y=3/3x
y=3x
To find the equation of a line through the origin, we first need to find the slope of the line using the two points (3,3) and (8,8).
Slope (m) = (y2 - y1) / (x2 - x1)
m = (8 - 3) / (8 - 3)
m = 5 / 5
m = 1
So, the equation of the line through the origin is y = 1x or simply y = x.
To find the equation of the line through the origin, we need to find the proportional relationship between inches and feet using the given coordinates.
First, we calculate the ratio of inches to feet for each point:
Point 1: (1 foot, 12 inches) ==> 12 inches/1 foot = 12
Point 2: (2 feet, 24 inches) ==> 24 inches/2 feet = 12
Point 3: (3 feet, 36 inches) ==> 36 inches/3 feet = 12
Since the ratio is the same for all points, the equation of the line through the origin is y = 12x.
To complete the table for the equation y = 5x, we can plug in the x-values and solve for the corresponding y-values.
For x = 0:
y = 5(0) = 0
(0,0)
For x = 1:
y = 5(1) = 5
(1,5)
For x = 2:
y = 5(2) = 10
(2,10)
Therefore, the completed table is:
(0,0), (1,5), (2,10) so the answer is d.(0,0),(1,5),(2,10).
To graph the proportional relationship y = -2x, we can plot the given points:
a. (0,0), (1,-2), (2,-4)
b. (0,0), (1,5), (2,10)
c. (0,0), (1,2), (2,4)
d. (0,0), (1,-1), (2,-2)
Plotting these points on a graph, we get the following:
a. (0,0), (1,-2), (2,-4) - This is the correct sequence for the proportional relationship y = -2x.
The points form a straight line passing through the origin (0,0) with a slope of -2. So the correct answer is a. (0,0), (1,-2), (2,-4).
All answers except "no, it's not the correct graph" are correct. the correct answer for 5 is "yes, it is the correct graph because the ordered pair (0,0) satisfies the equation. . ."
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
inches per feet. 1 foot, 4 inches.
graph coordinates: (1,12),(2,24),(3,36)
answers
y=2x
y=12x
y=36x
y=1/12x
complete the ordered pairs in the table by finding the y-value of the ordered pairs for the equation y=5x.
x,y,(x,y)
0,_,(0,_)
1,_,(1,_)
2,_,(2,_)
answers:
a.(0,0),(1,5),(3,15)
b.(0,0),(1,1/5),(2,2/5)
c.(0,0),(5,1),(10,2)
d.(0,0),(1,5),(2,10)
Graph the proportional relationship y=-2x by plotting points.
a. (0,0),(1,-2),(2,-4)
b. (0,0),(1,5),(2,10)
c. (0,0),(1,2),(2,4)
d. (0,0),(1,-1),(2,-2)
Is this the correct graph of the equation y=1/5x?
graph: (0,0),(5,1)
answers:
a. yes, it is the correct graph because the ordered pair (0,0) satisfies the equation and the slope m = rise/run = 1/5.
b. No, it is not the correct graph because the slope m = rise/run = 1/5.
c. Yes, it is the correct graph because the slope = 5/1.
d. No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 1/5 x.
Apologies for the oversight. Thank you for pointing that out.
Given the equation y = 1/5x and the points (0,0) and (5,1) on the graph:
Since the ordered pair (0,0) satisfies the equation y = 1/5(0) = 0, the correct answer is indeed:
a. Yes, it is the correct graph because the ordered pair (0,0) satisfies the equation and the slope m = rise/run = 1/5.