The equation of Line 1: 4x - 2y = 16

Question

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 2 has an increasing graph
Line 2 has an increasing graph

Line 3 has the greatest slope
Line 3 has the greatest slope

Line 2 has the biggest y-intercept
Line 2 has the biggest y-intercept

Line 1 has the biggest y-intercept
Line 1 has the biggest y-intercept

Line 3 has a decreasing graph
Line 3 has a decreasing graph

Line 1 has the greatest slope.

Answer 1

To evaluate which statement is true, we need to determine the slopes and y-intercepts of each line.

Line 1: \(4x - 2y = 16\)
We can rewrite this in slope-intercept form \(y = mx + b\):

1. Rearranging gives:
   \(-2y = -4x + 16\)
   \(y = 2x - 8\)

• Slope (m): 2
• Y-intercept (b): -8

Line 2: \(y = -\frac{4}{5}x + 2\)

• Slope (m): \(-\frac{4}{5}\)
• Y-intercept (b): 2

Line 3: \(y - 4 = 3(x + 5)\)
Rewrite it in slope-intercept form:

1. Expanding gives:
   \(y - 4 = 3x + 15\)
   \(y = 3x + 19\)

• Slope (m): 3
• Y-intercept (b): 19

Now we compare slopes and y-intercepts:

• Slopes:

  • Line 1: 2
  • Line 2: \(-\frac{4}{5}\) (decreasing)
  • Line 3: 3 (greatest slope)

• Y-intercepts:

  • Line 1: -8
  • Line 2: 2
  • Line 3: 19 (greatest y-intercept)

Now we can evaluate the statements:

1. Line 2 has an increasing graph - False (it has a negative slope)
2. Line 3 has the greatest slope - True (slope of 3)
3. Line 2 has the biggest y-intercept - False (Line 3 has the biggest y-intercept)
4. Line 1 has the biggest y-intercept - False (Line 3 has the biggest y-intercept)
5. Line 3 has a decreasing graph - False (it has a positive slope)
6. Line 1 has the greatest slope - False (Line 3 has the greatest slope)

Thus, the true statement is:

Line 3 has the greatest slope.