The equation of Line 1: 2x - 4y = 16
The equation of Line 2: y = - 3/4x -3
The equation of Line 3: y - 5 = -2 (x+1)
Which statement is true?
(2 points)
O Line 1 has the steepest slope.
O Line 3 has the least steep slope.
O Line 3 has a decreasing graph.
O Line 2 has the biggest y-intercept.
O Line 1 has the biggest y-intercept.
O Line 2 has an increasing graph.
The equation of Line 1: 2x - 4y = 16 can be rewritten as y = (1/2)x - 4. This means that Line 1 has a slope of 1/2.
The equation of Line 2: y = -3/4x - 3 has a slope of -3/4.
The equation of Line 3: y - 5 = -2 (x+1) can be rewritten as y = -2x - 3, which means that Line 3 has a slope of -2.
From the given slopes, it is clear that Line 3 has the least steep slope, so the statement "Line 3 has the least steep slope" is true.
However, none of the other statements are true based on the given information.
That’s not true
Apologies for the incorrect response. Let's reevaluate the statements based on the given equations:
The equation of Line 1: 2x - 4y = 16 can be rewritten as y = (1/2)x - 4. This means that Line 1 has a slope of 1/2.
The equation of Line 2: y = -3/4x - 3 has a slope of -3/4.
The equation of Line 3: y - 5 = -2 (x+1) can be rewritten as y = -2x - 3, which means that Line 3 has a slope of -2.
Now, comparing the slopes:
1/2 is greater than -3/4, which means Line 1 has a steeper slope than Line 2. Therefore, the statement "Line 1 has the steepest slope" is true.
-2 is the least steep slope out of 1/2, -3/4, and -2. Therefore, the statement "Line 3 has the least steep slope" is also true.
Based on the slopes, we cannot determine whether Line 3 has a decreasing graph or an increasing graph. Therefore, the statement "Line 3 has a decreasing graph" or "Line 3 has an increasing graph" cannot be determined.
As for the y-intercepts:
Line 1 has a y-intercept of -4, Line 2 has a y-intercept of -3, and Line 3 has a y-intercept of -3. Among these, Line 2 has the biggest y-intercept. Therefore, the statement "Line 2 has the biggest y-intercept" is true.
In conclusion, the correct statement is:
- Line 1 has the steepest slope.
- Line 3 has the least steep slope.
- Line 2 has the biggest y-intercept.
There is only one answer
Apologies for the confusion. Based on the given equations:
The equation of Line 1: 2x - 4y = 16 can be rewritten as y = (1/2)x - 4. This means that Line 1 has a slope of 1/2.
The equation of Line 2: y = -3/4x - 3 has a slope of -3/4.
The equation of Line 3: y - 5 = -2 (x+1) can be rewritten as y = -2x - 3, which means that Line 3 has a slope of -2.
Comparing the slopes:
1/2 is greater than -3/4, which means Line 1 has a steeper slope than Line 2. Therefore, the statement "Line 1 has the steepest slope" is true.
-2 is the least steep slope out of 1/2, -3/4, and -2. Therefore, the statement "Line 3 has the least steep slope" is also true.
Based on the slopes, we cannot determine whether Line 3 has a decreasing graph or an increasing graph. Therefore, the statement "Line 3 has a decreasing graph" or "Line 3 has an increasing graph" cannot be determined.
As for the y-intercepts:
Line 1 has a y-intercept of -4, Line 2 has a y-intercept of -3, and Line 3 has a y-intercept of -3. Among these, Line 2 and Line 3 have the same y-intercept. Therefore, the statement "Line 2 has the biggest y-intercept" or "Line 3 has the biggest y-intercept" cannot be determined.
Apologies for the mistake in my previous response. Based on the given information, we cannot determine which statement is true.
Summarize this
Based on the given equations:
Line 1 has a steeper slope than Line 2, and Line 3 has the least steep slope among the three lines.
The graph of Line 3 cannot be determined as increasing or decreasing based on the given information.
The statement regarding the y-intercepts of Line 2 and Line 3 cannot be determined with the given information.
Therefore, it is not clear which statement is true based on the given equations.