1. For the data in the table is why very directly with X if it does right now question for the direct variation x 10 y 15 x 16 y 24 x 30
2. The data in the table is why very directly affects if it does right in equation for the direct variation x 16 y 4 x 32 y 16 x 48 y 36
3. Match the equation with his graph 4x+6y=12
4. The equation with its graph 6x+8y=-3
#1 If I parse your garbled English correctly, y = 3/2 x
#2 same garbling, but y = (x/8)^2
#3,4 - no graphs; sorry. But there are lots of handy online graphing sites
Ty I used the microphone didn’t proof read sorry
1. To determine if the data in the table shows a direct variation, we need to check if there is a constant ratio between the values of X and Y. Let's calculate the ratios for each set of values:
1st set: X = 10, Y = 15
Ratio = Y/X = 15/10 = 1.5
2nd set: X = 16, Y = 24
Ratio = Y/X = 24/16 = 1.5
3rd set: X = 30, Y = ?
To find Y, we can use the ratio from the previous sets:
Ratio = Y/X = 1.5
Y = 1.5 * 30 = 45
Therefore, for the 3rd set, X = 30 and Y = 45.
Based on these calculations, we can see that there is a constant ratio of 1.5 between X and Y in all three sets. This indicates that the data shows a direct variation.
2. Similarly, let's calculate the ratios for each set of values:
1st set: X = 16, Y = 4
Ratio = Y/X = 4/16 = 0.25
2nd set: X = 32, Y = 16
Ratio = Y/X = 16/32 = 0.5
3rd set: X = 48, Y = ?
Using the ratio from the previous sets:
Ratio = Y/X = 0.5
Y = 0.5 * 48 = 24
Therefore, for the 3rd set, X = 48 and Y = 24.
Based on these calculations, we can see that the ratios between X and Y are not constant in each set. This indicates that the data does not show a direct variation.
3. To match the equation 4x + 6y = 12 with a graph, we need to rearrange the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
4x + 6y = 12 (rearranging the equation)
6y = -4x + 12 (isolating y)
y = (-4/6)x + 2 (dividing the equation through by 6)
Now we can identify the slope and y-intercept:
Slope (m) = -4/6 = -2/3
Y-intercept (b) = 2
The given equation represents a line with a slope of -2/3 and a y-intercept of 2. To match this equation with its graph, you can plot the y-intercept on the y-axis (point (0, 2)) and use the slope to find other points on the line.