4. Slope-Intercept Form: Examples

This lesson will discuss a few examples on the slope-intercept form of the equation of a line.

Example Find the equation of the line whose slope is 3 and y-intercept is 4.

Solution We already know the slope-intercept form of the equation:

y = mx + c

The slope m is given as 3. The y-intercept c is given as 4. Nothing much to do here then. The required equation will be

y = 3x + 4

Here’s how the line looks.

straight line slope intercept form

 

Example 2 Find the equation of the line which passes through a point on the Y-axis 5 units below the origin, and makes an angle of 45° with the X-axis.

Solution Here, “passes through a point on the Y-axis 5 units below the origin” is a fancy way to say that the y-intercept is -5.

And, “makes an angle of 45° with the X-axis” implies that the slope is tan45°, which equals 1.

By plugging in the values in the slope-intercept form, we’ll get the required equation as

y = 1x + (-5)

or

y = x – 5

Here’s how the line looks.

straight line slope intercept form

 

Example 3 A line passing through the origin has the slope as -2. Find its equation.

Solution Since the line passes through the origin, the y-intercept must be 0. Now, let’s use the slope-intercept form:

y = mx + c

On substituting the above values, we’ll get:

y  = -2x + 0

or

y = -2x

Here’s how the line looks.

straight line slope intercept form

That’s all for this lesson. The next one will discuss another form of the equation of the line, known as the intercept form.

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