equation 1: 4x-2y=16
equation 2: y=-4/5x+2
equation 3: y-4=3(x+5)
which statement is true?
A. line 1 has the greatest slope
B. line 2 has the biggest y intercept
C. line 2 has an increasing graph
D. line 1 has the biggest y intercept
E. line 3 has a decreasing graph
F. line 3 has the greatest slope
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's analyze each statement:
A. line 1 has the greatest slope
To find the slope of line 1, with the equation 4x - 2y = 16, we need to rearrange it into the slope-intercept form.
-2y = -4x + 16
Dividing by -2:
y = 2x - 8
The slope of line 1 is 2, which is not the greatest slope.
B. line 2 has the biggest y intercept
The y-intercept of line 2 is 2, which is bigger than the y-intercept of line 1 (which is -8). Therefore, this statement is true.
C. line 2 has an increasing graph
The slope of line 2 is -4/5, which is negative. A negative slope indicates a decreasing graph, not an increasing one. Therefore, this statement is false.
D. line 1 has the biggest y intercept
As mentioned earlier, the y-intercept of line 1 is -8, which is smaller than the y-intercept of line 2. Therefore, this statement is false.
E. line 3 has a decreasing graph
The slope of line 3, with the equation y - 4 = 3(x + 5), is 3, which is positive. A positive slope indicates an increasing graph, not a decreasing one. Therefore, this statement is false.
F. line 3 has the greatest slope
The slope of line 3 is 3, which is not the greatest slope. Therefore, this statement is false.
In conclusion, the only true statement is B. line 2 has the biggest y intercept.