Look at the graph shown:
A coordinate plane is shown. A line passes through the point -4 comma 1 and through the y-axis at 4.
Which equation best represents the line? (4 points)
y = 3 over 4.x + 4
y = 4 over 3.x + 4
y = 4x + 3 over 4.
y = 4x + 4 over 3.
To find the equation of the line passing through the point (-4, 1) and through the y-axis at 4, we need to determine the slope (m) and the y-intercept (b) of the line.
Given that the line passes through the y-axis at 4, the y-intercept is 4, which gives us the equation in the form y = mx + b.
To find the slope, we can use the formula (y2 - y1) / (x2 - x1) and substitute (-4, 1) for (x1, y1) and (0, 4) for (x2, y2):
m = (4 - 1) / (0 - (-4)) = 3 / 4.
Therefore, the equation of the line is y = (3/4)x + 4.
Hence, the correct equation that represents the line is y = 3/4.x + 4.
Two quantities are related, as shown in the table:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship? (4 points)
y = 1 over 2x + 2
y = 1 over 2x + 1
y = x + 2
y = 2x + 1
To determine the equation that best represents the relationship between the quantities x and y, we can observe the pattern in the given table.
As x increases by 2, y increases by 1. This indicates a constant rate of change, suggesting a linear relationship between x and y.
We can find the slope (m) by calculating the change in y divided by the change in x using any two points from the table:
m = (y2 - y1) / (x2 - x1) = (4 - 3) / (4 - 2) = 1 / 2.
From the table, we can see that the y-intercept (b) is 2 when x = 0.
Therefore, the equation that represents the relationship is y = (1/2)x + 2.
Hence, the correct equation that represents the relationship is y = 1/2x + 2.
4.
(05.02)
A line passes through (3, 7) and (6, 9). Which equation best represents the line? (4 points)
y = 3 over 2x + 5
y = 2 over 3x + 5
y = 3x + 2
y = 2 over 3x + 2
To find the equation of the line passing through the points (3, 7) and (6, 9), we need to determine the slope (m) and the y-intercept (b) of the line.
We can find the slope (m) by using the formula (y2 - y1) / (x2 - x1) and substituting the coordinates of the two points:
m = (9 - 7) / (6 - 3) = 2 / 3.
From here, we can find the y-intercept (b) by substituting the slope and one set of coordinates into the slope-intercept form of a linear equation, y = mx + b:
7 = (2/3)(3) + b
7 = 2 + b
b = 7 - 2
b = 5.
Therefore, the equation of the line is y = (2/3)x + 5.
Hence, the correct equation that represents the line is y = 2/3x + 5.
Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 3 and a horizontal side of 7. The other triangle has a vertical side of 9 and a horizontal side of 21.
Could the hypotenuses of these two triangles lie along the same line? (4 points)
Yes, because they are both right triangles
Yes, because they are similar triangles
No, because they are not similar triangles
No, because one is larger than the other
No, because they are not similar triangles.
rong it was
Yes, because they are similar triangles