1. find the relationship of x and y in the table.
x: 2; 4; 6; 8; 10
y: 1.5; 2; 3; 4.5; 5
y = _______ x + ________
2. find the relationship of x and y from a graph of a line that crosses the y-axis at y = 6 and that goes into the left 2 units and rises 3 units.
y = _______ x + _________
#1 I think you have a typo.
For x=4,6,10 y=x/2
For x=6,8 y=x/2 + 1/2
#2
crosses the y-axis at y = 6
y=mx+6
left 2 units and rises 3
m = 3/-2
so, y = -3/2 x + 6
sorry,
for question 1 its
x: 0; 1; 3; 6; 7
Oh, then it is clearly y=(x+3)/2
alright, thank you!
Can u guys help me out! With this!
x : 0 1 3 6 7
Y:1.5 2 3 4.5 5
Whats the realtionship!
To find the relationship between x and y in the given table, we need to examine the pattern of the values. The given table shows the values of x and y, corresponding to each other. Let's observe the changes in y as x increases.
In the given table:
x: 2; 4; 6; 8; 10
y: 1.5; 2; 3; 4.5; 5
We can see that as x increases by 2 each time, y increases by a factor of 0.5. We can express this relationship between x and y using the equation of a linear relationship, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
To determine the slope (m), we can calculate the change in y divided by the change in x.
Change in y = (4.5 - 1.5) = 3
Change in x = (6 - 2) = 4
Slope (m) = Change in y / Change in x
= 3 / 4
= 0.75
To find the y-intercept (b), we can take any point from the table and substitute it into the equation y = mx + b, then solve for b.
Using the point (2, 1.5):
1.5 = 0.75(2) + b
1.5 = 1.5 + b
b = 1.5 - 1.5
b = 0
Therefore, the equation relating x and y in the table is:
y = 0.75x + 0
Now, let's move on to the second question.
In the given graph, the line crosses the y-axis at y = 6 and goes 2 units to the left and 3 units up.
We can recognize that the slope of the line is the ratio of the vertical change (rise) to the horizontal change (run). In this case, the slope is 3/2 because the line goes up 3 units and left 2 units.
Using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is a point on the line, we can substitute the given values into the equation to find the relationship between x and y.
Using the point (0, 6):
y - 6 = (3/2)(x - 0)
Simplifying, we get:
y - 6 = (3/2)x
Rearranging the equation to the form y = mx + b:
y = (3/2)x + 6
Therefore, the relationship between x and y in the given graph is:
y = (3/2)x + 6