Question

The equation of Line 1:  4x - 2y = 16The equation of Line 2:  y = -4/5x + 2The equation of Line 3:  y - 4 = 3 (x + 5)Which statement is true?(1 point)ResponsesLine 3 has the greatest slopeLine 3 has the greatest slopeLine 3 has a decreasing graphLine 3 has a decreasing graphLine 1 has the greatest slope.Line 1 has the greatest slope.Line 2 has an increasing graphLine 2 has an increasing graphLine 2 has the biggest y-interceptLine 2 has the biggest y-interceptLine 1 has the biggest y-intercept

Answer 1

To determine which statement is true, let's analyze the slopes and y-intercepts of the three lines.

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

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

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

   • This line is already in slope-intercept form.
     • Slope (m) = -\(\frac{4}{5}\)
     • y-intercept (b) = 2

3. Line 3: \( y - 4 = 3(x + 5) \)

   • Rearranging to slope-intercept form: \[ y - 4 = 3x + 15 \implies y = 3x + 19 \]
     • Slope (m) = 3
     • y-intercept (b) = 19

Now, we can compare the slopes:

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

Comparing the slopes:

• Line 3 has the greatest slope (3).

Now comparing the y-intercepts:

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

Comparing the y-intercepts:

• Line 3 has the biggest y-intercept (19).

Now we can evaluate the statements:

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

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