Chapter 3 Notes Writing Linear Equations and Linear

3. 1 Writing Equations in Slope-Intercept Form ▪ Slope-intercept form is y = mx

3. 2 Writing Equations Using Slope and a Point ▪ First, plot the point

3. 3 Writing Equations Using Two Points ▪ Plot the points and draw a

3. 5 Writing A System of Linear Equations ▪ First, define your variables (What

Slides: 5

Download presentation

Chapter 3 Notes Writing Linear Equations and Linear Systems

3. 1 Writing Equations in Slope-Intercept Form ▪ Slope-intercept form is y = mx + b (m is the slope and b is the yintercept). ▪ First, choose any two points on the line and find the slope (slope is rise/run or change in y/change in x). ▪ Substitute the slope in for m. ▪ Second, use the graph to locate where the line crosses the y-axis (this is your y-intercept). ▪ Substitute the y-intercept in for b.

3. 2 Writing Equations Using Slope and a Point ▪ First, plot the point given on the graph. ▪ From that point, use the slope to find another point (slope is rise/run). ▪ From your new point, use your slope again to find the next point. ▪ Repeat the process until you can determine the y-intercept (you can also just draw a straight line through the first two points making sure that it crosses the y-axis). ▪ Once you have your slope and your y-intercept, write your equation in slope-intercept form (y=mx + b).

3. 3 Writing Equations Using Two Points ▪ Plot the points and draw a straight line through the two points. ▪ Find the slope (rise/run). ▪ Find the y-intercept (where the line crosses the y-axis). ▪ Write the equation in slope-intercept form (y = mx + b). ▪ To solve algebraically, first use the two points to find the slope. ▪ Plug it into your generic slope-intercept form equation. Use one of your points (x, y) to find the y-intercept (b). ▪ Write your equation in slope-intercept form (y = mx + b).

3. 5 Writing A System of Linear Equations ▪ First, define your variables (What is x? What is y? ). Second, write two equations showing how they are related. Third, write both equations in slope-intercept form. ▪ To solve by using a table, make a table of values to find the x-value that has the same y-value for both equations. That point (x, y) is the solution of the system of equations ▪ To solve by using a graph, use the slope and the y-intercept from each equation to graph two separate lines. The point (x, y) at which they cross is the solution of the system of equations. ▪ To solve algebraically, put the two equations (must be written in slopeintercept form) equal to each other. Solve for x. Once you have solved for x, plug it into either original equation and solve for y. The (x, y) combination is the solution of the system of equations.