The equation of Line 1: 4x - 2y = 16
The equation of Line 2: y = -4/5x + 2
The equation of Line 3: y - 4 = 3 (x + 5)
Which statement is true?
(1 point)
Responses
Line 3 has the greatest slope
Line 3 has the greatest slope
Line 1 has the biggest y-intercept
Line 1 has the biggest y-intercept
Line 2 has the biggest y-intercept
Line 2 has the biggest y-intercept
Line 1 has the greatest slope.
Line 1 has the greatest slope.
Line 3 has a decreasing graph
Line 3 has a decreasing graph
Line 2 has an increasing graph
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To determine which statement is true, we need to analyze the equations of the lines.
The slope-intercept form of a line is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Line 1: 4x - 2y = 16
To put this equation in slope-intercept form, we need to solve for y:
-2y = -4x + 16
y = 2x - 8
Comparing this equation with the slope-intercept form, we can see that the slope (m) is 2 and the y-intercept (b) is -8.
Line 2: y = -4/5x + 2
This equation is already in slope-intercept form, so we can identify that the slope (m) is -4/5 and the y-intercept (b) is 2.
Line 3: y - 4 = 3(x + 5)
To put this equation in slope-intercept form, we need to simplify it:
y - 4 = 3x + 15
y = 3x + 19
Comparing this equation with the slope-intercept form, we can see that the slope (m) is 3 and the y-intercept (b) is 19.
Now, let's evaluate each statement:
Line 3 has the greatest slope: False. Line 1 has the greatest slope with a value of 2.
Line 1 has the biggest y-intercept: False. Line 3 has the biggest y-intercept with a value of 19.
Line 2 has the biggest y-intercept: False. Line 3 has the biggest y-intercept with a value of 19.
Line 1 has the greatest slope: True. Line 1 has the greatest slope with a value of 2.
Line 3 has a decreasing graph: False. Line 3 has a positive slope of 3, indicating an increasing graph.
Line 2 has an increasing graph: True. Line 2 has a negative slope of -4/5, indicating a decreasing graph.
Based on our analysis, the correct statement is:
Line 2 has an increasing graph.
a b c or d
In this case, the correct statement is:
c) Line 2 has an increasing graph.