Linear Equations and Special Cases

# Linear Equations and Special Cases - MAC1105 Linear...

This preview shows pages 1–2. Sign up to view the full content.

MAC1105: Linear Equations and Special Cases If we are given two data points (or one data point and slope) that are part of a linear relationship, there are several procedures for deriving a linear equation of form y b mx = + = + = + = + or y mx b = + = + . Suppose we are given two data points, (3,2) and (5,14) . We first compute the slope: y 14 2 12 m 6 x 5 3 2 - = = = = - triangle triangle . Note that if we had been given a point and a slope, we would begin at this point. Now that we know the slope there are two ways to finish deriving the equation. 1) We now know that m 6 = , so we have the equation y b 6x = + = + . Substitute into this equation values from a data point and solve for the unknown b as follows. y b 6x (14) b 6(5) 14 b 30 b 16 = + = + = + = - = . We have derived the equation y 16 6x = - + . 2) Plug either data point and the slope into the point-slope formula 1 1 y m(x x ) y = - + . y 6(x 5) 14 y 6x 30 14 y 6x 16 = - + = - + = - . --------------------------------------------------------------------------------------------------------------------------------------- 1) Lines that pass through the origin. Lines whose graphs pass through the origin (0,0) have a y-intercept = 0, so the equations of these lines are very simple, y mx = .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern