2.3+Graph+Equations+of+Lines

A //family of functions// is a group of functions with shared characteristics. The **parent function** is the most basic function in a family. =**Parent Functions for Linear Functions**= The parent functions for the family of all linear functions is f(x)=x.

In general, a y-intercept of a graph is the y-coordinate of a point where the graph intersects the y-axis.\

Step 1 - Write the equation in slope-intercept form by solving for //y//.
Step 2 - Identify the //y//-intercept //b// and use it to plot the point //(0//,//b//) where the line crosses the //y//-axis Step 3 - Identify the slope //m// and use it to plot a second point on the line. Step 4 - Draw a line through the two points.

=Graphing from slope-intercept form=

The y-intercept is the y-value when the x-value is 0. If the y-intercept is 2, this means that it is plotted on the graph at //(0,2).// To graph using slope-intercept form, you first plot the y intercept, and then you account for the slope. If the formula is y=2x+1, then 2x is the slope and 1 is the y-intercept. You will plot the y-intercept at (0,1). Then, because the slope is 2, for every time the x-value increases by one, the y-value will increase by 2. 2(rise)/1(run) = 2, proving that the slope is 2.



Standard Form
The standard form of a linear equation is //Ax + By = C// where //A// and //B// are not zero. You can graph an equation in standard form by identifying and plotting the //x-// and //y-// intercepts. An //x//-intercept is the //x//-coordinate of a point where a graph intercects the //x//-axis.

Using Standard Form to Graph an Equation
Step 1 - Write the equation in standard form. Step 2 - Identify the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis. Step 3 - Identify the y-intercept by by letting x = 0 and solving solving for y. Use the y-intercept to plot the point where the line crosses the y-axis. Step 4 - Draw a line through the two points.

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