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?
a. line 2 has the biggest y-intercept
b. line 3 has a decreasing graph
c. line 2 has an increasing graph
d. line 3 has the least steep slope
e. line 1 has the biggest y-intercept
f. line 1 has the steepest slope
To determine which statement is true, let's analyze each option:
a. Line 2 has the biggest y-intercept.
The y-intercept of Line 2 is -3, which means the y-coordinate where the line intersects the y-axis is -3. Given the information provided, we cannot determine whether this y-intercept is the largest among the three lines.
b. Line 3 has a decreasing graph.
The equation of Line 3 is y - 5 = -2(x + 1), which can be rearranged to y = -2x - 3. Since the coefficient of x is negative (-2), the graph of Line 3 is indeed decreasing. Therefore, this statement is true.
c. Line 2 has an increasing graph.
The equation of Line 2 is y = 3/4x - 3. The coefficient of x is positive (3/4), indicating that the graph of Line 2 is increasing. Therefore, this statement is true.
d. Line 3 has the least steep slope.
The slope of Line 3 is -2. Given the information provided, we cannot compare this slope to the slopes of Line 1 and Line 2 in order to determine which is the least steep. Therefore, we cannot conclude that this statement is true.
e. Line 1 has the biggest y-intercept.
The equation of Line 1 is 2x - 4y = 16, which can be rearranged to y = 1/2x - 4. The y-intercept of Line 1 is -4, which is smaller than the y-intercept of Line 2 (-3). Therefore, this statement is false.
f. Line 1 has the steepest slope.
The slope of Line 1 is 1/2. Given the information provided, we cannot compare this slope to the slopes of Line 2 and Line 3 in order to determine which is the steepest. Therefore, we cannot conclude that this statement is true.
From the given options, the true statements are:
b. Line 3 has a decreasing graph.
c. Line 2 has an increasing graph.
i can only choose 1 is it B or C?
If you can only choose one statement, the correct answer would be:
c. Line 2 has an increasing graph.