2. Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: 𝑦=𝑚𝑥+𝑏, Point-Slope Form: 𝑦−𝑦1=𝑚(𝑥−𝑥1), and Standard Form: 𝐴𝑥+𝐵𝑦=𝐶. Each form allows for quick and easy ways to graph the line they represent. Forms of Linear Equations
3. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable, Calculate the corresponding value for the y-coordinate, and Repeat. In this way, we can create a table of ordered pairs and plot them on the coordinate plane. Make a Table
4. Consider the equation 𝑦=12𝑥+2. Make a Table 𝑦=12(−𝟐)+2 (-2,1) =1 𝑦=12(𝟎)+2 =2 (0, 2) 𝑦=12(𝟐)+2 (2, 3) =3
5. Another method for graphing lines when an equation is in slope-intercept form is as follows: Plot the y-intercept on the coordinate plane; that's the point (0, b). Use the slope to find another point (and repeat). Draw a line through the points. Use the slope and intercept
6. Consider the equation𝑦=−54𝑥+7. Plot the y-intercept Use the slope to find another point (and repeat). Draw a line through the points. Use the slope and intercept (0, b) = (0, 7) From the intercept, move down 5 and right 4 (or up 5 and left 4).
7. This method is very similar to the slope-intercept method. To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1). Use the slope to find another point (and repeat). Draw a line through the points. Use a point and the slope
8. Consider the equation𝑦−2=73(𝑥+3). Plot the point (𝑥1, 𝑦1) Use the slope to find another point (and repeat). Draw a line through the points. Use a point and the slope (𝑥1, 𝑦1)= (-3, 2) From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.
9. This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶). The x-intercept is easily calculated by setting y to 0 and solving for 𝑥. The y-intercept is calculated by setting 𝑥 to zero and solving for 𝑦. Plot the two intercepts and draw a line through them. Use the Intercepts
10. Consider the equation3𝑥−5𝑦=−15. Set 𝑦=0 and solve for 𝑥. Set 𝑥=0 and solve for 𝑦. Draw a line through the points. Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0) −5𝑥=−15; 𝑦=3(0, 3)
