Derive Slope-Intercept Formula

harpazo

Pure Mathematics
Banned
How do we derive the slope-intercept formula in the picture?

MarkFL

La Villa Strangiato
Staff member
Moderator
Math Helper
The point-slope formula may be written as:

$$\displaystyle y=mx+y_1-mx_1$$

We see that when $$x=0$$, we have:

$$\displaystyle y=y_1-mx_1$$

And so we know the $$y$$-intercept is $$\left(0,y_1-mx_1\right)$$

If we define:

$$\displaystyle b=y_1-mx_1$$

Then, the $$y$$-intercept is at $$(0,b)$$, and the line can be written as:

$$\displaystyle y=mx+b$$

Or, we could begin by saying the $$y$$-intercept is at the point on the $$y$$-axis $$(0,b)$$ and so a line having slope $$m$$, will be described by (using the point-slope formula):

$$\displaystyle y-b=m(x-0)$$

Or:

$$\displaystyle y=mx+b$$

anemone and harpazo

harpazo

Pure Mathematics
Banned
The point-slope formula may be written as:

$$\displaystyle y=mx+y_1-mx_1$$

We see that when $$x=0$$, we have:

$$\displaystyle y=y_1-mx_1$$

And so we know the $$y$$-intercept is $$\left(0,y_1-mx_1\right)$$

If we define:

$$\displaystyle b=y_1-mx_1$$

Then, the $$y$$-intercept is at $$(0,b)$$, and the line can be written as:

$$\displaystyle y=mx+b$$

Or, we could begin by saying the $$y$$-intercept is at the point on the $$y$$-axis $$(0,b)$$ and so a line having slope $$m$$, will be described by (using the point-slope formula):

$$\displaystyle y-b=m(x-0)$$

Or:

$$\displaystyle y=mx+b$$
How important is this topic in calculus 1?

MarkFL

La Villa Strangiato
Staff member
Moderator
Math Helper
Being able to do simple analytic geometry is extremely important in the study of calculus.

harpazo

Pure Mathematics
Banned
Being able to do simple analytic geometry is extremely important in the study of calculus.
There's a chapter in Sullivan's College Algebra dedicated to Conics.

Staff member