The slope of the line given by the equation \( y = -\frac{4}{3}x \) is \( -\frac{4}{3} \).
To determine how the line was shifted to obtain the graph of \( y = -43x - 5 \), we need to first identify the slope and y-intercept of both lines.
The equation \( y = -43x - 5 \) has:
- Slope = \( -43 \)
- Y-intercept = \( -5 \)
The change in slope from \( -\frac{4}{3} \) to \( -43 \) indicates a significant steepening of the line. However, there's likely a misunderstanding regarding the slope because from the manipulation of these two equations, we could infer a scaling error rather than a simple shift, as slopes are not transformed linearly via shifts.
To find out how the y-intercept shifted:
- The original line has a y-intercept of 0 (since \( y = -\frac{4}{3}x \) intersects the y-axis at 0).
- The new line has a y-intercept of \( -5 \).
Thus, the line has been vertically shifted downwards by \( 5 \) units.
In summary:
- The slope of the line is \( -\frac{4}{3} \).
- The line was shifted downward by \( 5 \) units.