What happens to a line when the y-intercept is changed? Check all that apply. A. As the y-intercept increases, the graph of the
line shifts up. B. as the y-intercept decreases, the graph of the line shifts left. C. As the y-intercept increases, the graph of the line gets steeper. D. As the y-intercept decreases, the graph of the line shifts down. E. as the y-intercept increases, the graph of the line shifts right.
<span>Answer: two options apply: A and D. </span> <span /><span /><span>A. As the y-intercept increases, the graph of the line shifts up.
D. As the y-intercept decreases, the graph of the line shifts down. </span><span />
<span>Justification:
</span><span>1) Take the slope-intercept equation of the line: y = f(x) = mx + b</span> <span /><span> </span><span>2) The y-intercept is b </span> <span /><span /><span> 3) When b is increased, f(x) will increases too, that is f(x) will be higher or its graph will be shifted up, which is what the option A. states. </span><span />
<span>4) When b is decreased, f(x) will decreases too, that is f(x) will be lower or its graph will be shifted dOwn, which is what the option D states. </span><span />
<span>5) Regarding the options B and E, which deal with motions in the horizontal direction (left or righT), nothing can be said, as the effect of a change in the y -intercept on the horizontal direction will depend on the slope. </span><span />
<span>6) Regarding the option C, a change in the y-intercept does not change the slope (the steep of the line). </span><span />
