# 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