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

The equation of Line 2: y=-4/5x+2
The equation of Line 3: y-4=3(x+5)
Which statement is true?

Line 3 has the greatest slope
Line 3 has a decreasing graph
Line 2 has an increasing graph
Line 1 has the biggest y-intercept
Line 2 has the biggest y-intercept
Line 1 has the greatest slope

1 answer

To evaluate the statements about the lines, we need to analyze the slopes and y-intercepts of all three lines.

Line 1: \(4x - 2y = 16\)

Convert to slope-intercept form (y = mx + b): \[ -2y = -4x + 16 \implies y = 2x - 8 \]

  • 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: \(y - 4 = 3(x + 5)\)

Convert to slope-intercept form: \[ y - 4 = 3x + 15 \implies y = 3x + 19 \]

  • Slope (m) = 3
  • y-intercept (b) = 19

Now, let's analyze the slopes and y-intercepts:

  • Slopes:

    • Line 1: Slope = 2
    • Line 2: Slope = -\(\frac{4}{5} \approx -0.8\) (decreasing)
    • Line 3: Slope = 3 (greatest slope)
  • y-intercepts:

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

Now, checking each statement:

  1. Line 3 has the greatest slope: True (Slope = 3)
  2. Line 3 has a decreasing graph: False (Slope = 3, which is increasing)
  3. Line 2 has an increasing graph: False (Slope = -\(\frac{4}{5}\), which is decreasing)
  4. Line 1 has the biggest y-intercept: False (y-intercept = -8, Line 3 has the largest y-intercept)
  5. Line 2 has the biggest y-intercept: False (Line 3 has the largest y-intercept)
  6. Line 1 has the greatest slope: False (Line 3 has the greatest slope)

Final answer: The only true statement is "Line 3 has the greatest slope."