Final answer:
Increasing the slope of a linear equation causes the line to rotate counter-clockwise around the y-intercept without altering the x or y intercepts. Increasing the y-intercept shifts the whole line vertically upwards, altering the position of the x-intercept but keeping the slope the same.
Step-by-step explanation:
The question seems to refer to the effect of changes in the slope and y-intercept on the graph of a linear equation. In linear equations of the form y = mx + b, the slope (m) determines the steepness or inclination of the line, while the y-intercept (b) is the point where the line crosses the y-axis.
When we increase the slope while keeping the y-intercept constant, the line will rotate counter-clockwise around the y-intercept. This can be visualized as the line becoming steeper if the slope was positive, or less steep if the slope was negative. However, it does not shift the position of the x or y-intercepts themselves.
Conversely, when we increase the y-intercept while keeping the slope constant, the entire line moves vertically upwards. That means the y-intercept increases, but the x-intercept will change depending on the slope's sign and magnitude since the line moves as a whole unit. The slope of the line will remain unchanged by this adjustment.