Question

Given the two equations of a line:

f(x) = -4x-5

g(x)=-2x+6

select the true statement

a
the slope of f(x) is greater than g(x)

b
the y intercept of g(x) is greater than f(x)

c
g(x) slope is greater than f(x)

d
the y intercept of f(x) is greater than g(x)

Answer 1

To analyze the two equations of the lines, we need to identify the slopes and y-intercepts for both functions.

For \( f(x) = -4x - 5 \):
- Slope (m) = -4
- Y-intercept (b) = -5 (when \( x = 0 \))

For \( g(x) = -2x + 6 \):
- Slope (m) = -2
- Y-intercept (b) = 6 (when \( x = 0 \))

Now, let's evaluate the statements:

**a)** The slope of \( f(x) \) is greater than \( g(x) \).
- \( -4 \) (slope of \( f(x) \)) is not greater than \( -2 \) (slope of \( g(x) \)), so this statement is **false**.

**b)** The y-intercept of \( g(x) \) is greater than \( f(x) \).
- \( 6 \) (y-intercept of \( g(x) \)) is greater than \( -5 \) (y-intercept of \( f(x) \)), so this statement is **true**.

**c)** The slope of \( g(x) \) is greater than \( f(x) \).
- \( -2 \) (slope of \( g(x) \)) is greater than \( -4 \) (slope of \( f(x) \)), so this statement is **true** as well.

**d)** The y-intercept of \( f(x) \) is greater than \( g(x) \).
- \( -5 \) (y-intercept of \( f(x) \)) is not greater than \( 6 \) (y-intercept of \( g(x) \)), so this statement is **false**.

Based on this analysis, the true statements are:

- **b)** The y-intercept of \( g(x) \) is greater than \( f(x) \).
- **c)** The slope of \( g(x) \) is greater than \( f(x) \).

If you only want one answer, **b** is true and is complete in itself.