To find the equation of a linear function with a slope of 45 and a y-intercept of -6, we can use the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Given:
- Slope \( m = 45 \)
- Y-intercept \( b = -6 \)
Substituting these values into the equation, we get:
\[ y = 45x - 6 \]
Now we can look at the responses given:
- \( 6x + 45y = 6 \)
- \( y = \frac{4}{5}x + 6 \)
- \( y = 45x - 6 \)
- \( y = \frac{4}{5}x - 6 \)
- \( y = -6x + 45 \)
Among the options, the correct equation that represents a linear function with the given slope and y-intercept is:
\( y = 45x - 6 \)
So the answer is option 3: \( y = 45x - 6 \).