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)
Responses
Line 1 has the steepest slope.
Line 1 has the steepest slope.
Line 3 has a decreasing graph.
Line 3 has a decreasing graph.
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 2 has an increasing graph.
Line 2 has an increasing graph.
Line 3 has the least steep slope.
Line 1 has the steepest slope.
Line 3 has a decreasing graph.
Line 1 has the biggest y-intercept.
Line 2 has an increasing graph.
Line 3 has the least steep slope.
Out of these statements, only Line 1 has the steepest slope and Line 3 has a decreasing graph. The statement "Line 1 has the biggest y-intercept" is not true as Line 2 has the biggest y-intercept. The statement "Line 2 has an increasing graph" is also not true as Line 2 has a negative slope and therefore has a decreasing graph. The statement "Line 3 has the least steep slope" is not true as Line 2 has the least steep slope.
That’s not right
My apologies for the incorrect response. Let's analyze the given equations to determine the true statements.
The equation of Line 1: 2x - 4y = 16
This equation can be rewritten as y = (1/2)x - 4. Therefore, Line 1 has a slope of 1/2 and a y-intercept of -4.
The equation of Line 2: y = -3/4x - 3
This line has a slope of -3/4 and a y-intercept of -3.
The equation of Line 3: y - 5 = -2(x + 1)
Simplifying, we get y = -2x - 7. This means that Line 3 has a slope of -2 and a y-intercept of -7.
Now let's analyze the statements:
1. Line 1 has the steepest slope: False. Line 2 has the steepest slope with a value of -3/4.
2. Line 3 has a decreasing graph: True. As the slope of Line 3 is negative (-2), it has a decreasing graph.
3. Line 1 has the biggest y-intercept: False. Line 2 has the biggest y-intercept with a value of -3.
4. Line 2 has the biggest y-intercept: True. Line 2 has a y-intercept of -3, which is greater than the y-intercept of Line 1 (-4) and Line 3 (-7).
5. Line 2 has an increasing graph: False. As the slope of Line 2 is negative (-3/4), it has a decreasing graph.
6. Line 3 has the least steep slope: False. Line 1 has the least steep slope with a value of 1/2.
Therefore, the true statements are:
- Line 3 has a decreasing graph.
- Line 2 has the biggest y-intercept.