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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?

(1 point)
Responses

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

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

Line 2 has an increasing graph
Line 2 has an increasing graph

Line 1 has the greatest slope.
Line 1 has the greatest slope.

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

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

Let's analyze each line's equation to find the slope and y-intercept.

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

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

  • 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: \(y - 4 = 3(x + 5)\)

First, expand this equation: \[ y - 4 = 3x + 15 \] \[ y = 3x + 19 \]

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

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

  1. Line 1: Slope = 2, Y-intercept = -8
  2. Line 2: Slope = -\(\frac{4}{5}\), Y-intercept = 2
  3. Line 3: Slope = 3, Y-intercept = 19

Now we can evaluate each statement:

  1. Line 1 has the biggest y-intercept. - False (Line 3 has the biggest y-intercept of 19).
  2. Line 3 has the greatest slope. - True (Line 3 has the slope of 3, which is greater than 2 and -\(\frac{4}{5}\)).
  3. Line 2 has an increasing graph. - False (Line 2 has a negative slope).
  4. Line 1 has the greatest slope. - False (Line 3 has the greatest slope).
  5. Line 3 has a decreasing graph. - False (Line 3 has a positive slope).
  6. Line 2 has the biggest y-intercept. - False (Line 3 has the biggest y-intercept).

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