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Find the slope and the -intercept of the following lines.
The line is in the slope-intercept form
The slope is
, the coefficient of
. Therefore,
The
is the point
Since
, the
is
The line is in slope-intercept form
The slope is
, the coefficient of
. So,
The
is the point
Since
, the
is
The equation is written in general form. We can put the equation in slope-intercept form by solving for
.
Now the equation is in slope-intercept form.
We have observed that the slope is a measure of the steepness of a line. We wish to develop a formula for measuring this steepness.
It seems reasonable to develop a slope formula that produces the following results:
Steepness of line steepness of line 2.
Consider a line on which we select any two points. We’ll denote these points with the ordered pairs and . The subscripts help us to identify the points.
is the first point. Subscript 1 indicates the first point.
is the second point. Subscript 2 indicates the second point.
The difference in values gives us the horizontal change, and the difference in values gives us the vertical change. If the line is very steep, then when going from the first point to the second point, we would expect a large vertical change compared to the horizontal change. If the line is not very steep, then when going from the first point to the second point, we would expect a small vertical change compared to the horizontal change.
We are comparing changes. We see that we are comparing
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