Question

When graphing a linear function in slope-intercept form, why do you have to plot the y-intercept first? Why can't you use the slope first?

Answer 1

In graphing a linear equation in slope-intercept form, the y-intercept provides a precise starting point on the y-axis, while the slope describes the line's rise over run from that starting point.

Step-by-step explanation:

When graphing a linear function in slope-intercept form, the conventional approach is to plot the y-intercept first. The y-intercept is where the line crosses the y-axis. In the slope-intercept form of a linear equation, y = mx + b, m represents the slope and b represents the y-intercept. By starting with the y-intercept, you establish a starting point for the line at the value of y when x is zero.

From there, you can use the slope, which describes how the line rises or falls as you move along the x-axis, to find another point on the line. Because the y-intercept is a specific point that directly corresponds to the y-axis, it provides a precise location to commence plotting your line. In contrast, the slope represents a ratio of the change in y (rise) over the change in x (run), and without a starting point, such as the y-intercept, it can't provide a specific location on the graph.

Answer 2

Because the slope doesn't tell you any actual points on the line.
It only tells you whether the line tilts up or down, and how steeply.
But the line could be way up there or way down under, with the same slope.
You can't actually DRAW it until you know some point on it, and
the y-intercept gives you one.