**Interactive Instructions:**Slope-intercept form:

*y = mx + b*. Move the green points to change

*m*and

*b*.

[

**NOTES**: Slope and y-Intercept ]
Showing posts with label **Y-intercept**. Show all posts

Showing posts with label **Y-intercept**. Show all posts

[ **NOTES**: Slope and y-Intercept ]

You might be familiar with the basic fact that two points determine a line. This fact leads to a nice and easy way to graph lines using the two points called the *x*- and *y*-intercepts.

All*x*-intercepts, if they exist, must have a corresponding *y*-value of zero. All *y*-intercepts must have a corresponding *x*-value of zero. This might sound confusing but just remember the following steps to algebraically find intercepts.

**Example**: Graph 3*x* − 5*y* = 15 using the *x*- and *y*-intercepts.

**Instructional Video**: Graphing by Finding Intercepts

This is a nice and easy method for determining the two points you need for graphing a line. In fact, we will use this exact technique for finding intercepts when we study the graphs of all the conic sections later in our study of Algebra. Be careful not to say that*y* = −3 is the *y*-intercept because the intercepts, actually, are ordered pairs or points on the graph so you should take care to say (0,−3) is the *y*-intercept.

**Use the given graph to answer the question.**

**Example**: Graph −4*x* + 3*y* = 12 using the intercepts.

**Example**: Graph −4*x* + 2*y* = −6 using the intercepts.

**Example**: Graph *y* = −5*x* +15 using the intercepts.

**Example**: Graph *y* = −3/4 *x* + 9 using the intercepts.

This brings us to one of the most popular questions in linear graphing.**Do all lines have ***x*- and *y*-intercepts? The answer is NO. Horizontal lines, of the form *y* = *b*, do not necessarily have *x*-intercepts. Vertical lines, of the form *x* = *a*, do not necessarily have *y*-intercepts.

**Example**: Graph *y* = 3.

**Example**: Graph* x* = −2.

**Video Examples on YouTube**:

All

Plot the points and draw a line through them with a straight edge.

This is a nice and easy method for determining the two points you need for graphing a line. In fact, we will use this exact technique for finding intercepts when we study the graphs of all the conic sections later in our study of Algebra. Be careful not to say that

Be sure to pay attention to the scale. Misreading the scale is the most common error in this type of problem.

This brings us to one of the most popular questions in linear graphing.

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