Question

Suppose you were sketching the graph of y X + 2, Why does it make sense to begin with the y-intercept instead of the slope?

(help me out please)​

Answer 1

Explanation:

When graphing a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept, it makes sense to begin with the y-intercept instead of the slope because the y-intercept gives us a point on the y-axis where the line crosses it.

In the case of the equation y = X + 2, the y-intercept is the point (0,2) on the y-axis, which is a point we can easily plot on the graph. Once we have plotted the y-intercept, we can then use the slope, which is 1 in this case, to find another point on the line by moving one unit to the right along the x-axis and one unit up along the y-axis. We can then draw a straight line through these two points to complete the graph of the line.

Starting with the y-intercept also makes sense because it gives us a sense of the vertical position of the line before we consider its slope. This can be helpful in cases where the y-intercept is a large or small number, as it can affect the scale of the graph and make it easier to read. Additionally, starting with the y-intercept can help us to quickly identify whether the line intersects the y-axis or not, and at what point.

Answer 2

It makes sense to begin with the y-intercept when sketching the graph of y = mx + b because the y-intercept is the point at which the line intersects the y-axis, where x = 0. This point gives us a starting point for the graph and allows us to plot a single point before determining the slope of the line. Once we have the y-intercept, we can use the slope to find additional points on the line, and then connect the points to create the graph of the line.