Slope-Intercept Form

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An equation is in slope-intercept form, if it is in the form:

y = mx + b

The graph of the equation will always be a straight line with a slope of m and a y-intercept of (0, b).

Example 1

Determine the slope and y-intercept of the following line:

-4x + 2y = 16

Solution

Write the original equation in slope-intercept form by adding 4x to each side and then dividing everything by two:

-4x + 2y + 4x = 16 + 4x

(2y) ÷ 2 = (4x + 16) ÷ 2

y = 2x + 8

 

The slope is 2.  The y-intercept is 8, or (0, 8).

You can also use the slope and y-intercept to graph a line.

Example 2

Graph the equation: y = ¹/₂x + 2

Solution

Using the slope-intercept form we see that the y-intercept is 2, so the first point is at (0, 2)

The slope is ¹/₂, so we can plot a second point by moving up 1 unit and then to the right 2 units.

Finally we draw a line through both points.

1.    Find the x- and y-intercepts, slope and graph of 6x + 5y = 30.

 

 

 

2.    Find the x- and y-intercepts, slope and graph of x = 3.

 

 

 

3.    Find the x- and y-intercepts, slope and graph of y = -4.

 

 

 

 

4.    Write in slope-intercept form the line that passes through the points (4, 6) and (−4, 2).

 

 

 

 

5.    Write in slope-intercept form the line parallel to the graph of x + 4y = −1 and containing the point (2, 3).  (Hint: Parallel lines have the same slope.)