Jennifer S. answered • 08/13/25
Math Professor With 17 Years Teaching and 30 Years Tutoring Experience
Hi there. I'm not sure if I fully understand your question, but If you have a different slope, the graph will either be steeper or shallower in the same direction if it's the same sign, or if it's the opposite sign, it will point the other way.
So, for example, if your slope is positive, say m = 3, then your line will increase up toward the right, meaning it will go higher as it moves right.. Now, if you make the slope a smaller positive number, say m = 2, then the line will still increase up toward the right, but it wont' be as steep. If you have a larger postive slope, say m = 4, then the line will increase up toward the right and be steeper than the original line.
If your m = 0, then the line will be horizontal.
Now, if you change the slope to a negative, then it will decrease toward the right, meaning the right side will go lower, not higher.
As for the y-intercept, this is the ordered pair where the graph touches or crosses the y-axis. In y = mx + b, the y-intercept is (0,b). Some say it's just b, but it really is an ordered pair.
If your (0, b) = (0, 2), then the graph will cross at that point. If you move it to (0, 5), the line will instead go through that point, which is higher, so the line will move up. If you move to (0, 1), the line will instead go down.
Now, if you want a "solution", I'm not sure what you mean by that. If you have y = 5x + 7, and you say x = 2, then y = 5(2) + 7 = 17. Therefore, (2, 17) is a point on the line, otherwise known as a solution.
Please let me know if I did not answer your question. If not, please clarify. Thanks!
