ºÝºÝߣ

ºÝºÝߣShare a Scribd company logo

Do you know the line

?Download as PPTX, PDF?
?
M
Matthew DeMoss

This document provides information and examples about linear equations and slope. It defines linear equations as straight lines that can be represented using slope-intercept, point-slope, or general form. Slope is defined as the measure of steepness of a line and is calculated using two points. Examples are provided for finding the slope and equation of a line. The document also discusses parallel and perpendicular lines and provides examples of finding equations of lines with those relationships.

1 of 12
Download to read offline
DO YOU KNOW THE LINE? Tackle the Math All Things Lines
Example of Linear Equation ¡ö Linear equations are always straight lines when graphed. ¡ö They always fit the following formulas: ¨C Slope-intercept form: ? = ?? + ?, where m is the slope and b is the y-intercept. ¨C Point-slope form: ? ? ?1 = ?(? ? ?1), where m is the slope and ?1, ?1 is a point. ¨C General form: ?? + ?? = ? ¡ö Slope-intercept form and point-slope form are by far the most common.
Slope ¡ö The ¡°slope¡± of a line is the measure of its steepness. ¡ö Other terms for slope are average rate of change and rise over run ¡ö The equation for slope is as follows: ¨C ? = ?2??1 ?2??1 ¨C To find the slope, you must have two points ?1, ?1 ??? ?2, ?2 .
Slope Example Find the slope of a line with points (1, 3) and (4, 12). ¡ö First, determine ?1, ?1 ??? ?2, ?2 . ¡ö ?1 = 1, ?1 = 3, ?2 = 4, ??? ?2 = 12. ¡ö Now let¡¯s use the slope equation. ¡ö ? = ?2??1 ?2??1 ¡ö ? = 12?3 4?1 ¡ö ? = 9 3 ¡ö ? = 3
Equation Example Find the equation of a line which has a slope of 2 and goes through the point (1, 5). ¡ö Since we already know the slope, it would be prudent to use slope-intercept form: ? = ?? + ?. m = 2.We do not, however, know the y-intercept (b).This is not a problem.We can replace m, x, and y with the slope and point given. ¡ö ? = ?? + ? ¡ö 5 = 2 1 + ?. Now we solve for b. ¡ö 5 = 2 + ? ¡ö 3 = ?. Now we have everything we need! Let¡¯s plug in m and b to slope-intercept form. ¡ö ? = 2? + 3
Equation Example 2 ¡ö ? = 8?0 2?(?2) = 8 4 = 2 ¡ö ? = 2? + ? ¡ö 0 = 2 ?2 + ? ¡ö 0 = ?4 + ? ¡ö 4 = ? ¡ö ? = 2? + 4 Find the equation of the line passing through the points (-2, 0) and (2, 8). Slope-Intercept ? = ?? + ? Point-Slope ? ? ?1 = ? ? ? ?1 ¡ö ? = 8?0 2?(?2) = 8 4 = 2 ¡ö ? ? ?1 = 2 ? ? ?1 ¡ö ? ? 8 = 2 ? ? 2 ¡ö ? ? 8 = 2? ? 4 ¡ö ? = 2? + 4
Parallel Lines ¡ö Lines are considered parallel when they never touch. ¡ö Algebraically, they have the same slope. ¡ö If you¡¯re given a problem which says, ¡°Find the equation of a line passing through the point (1, 2) and parallel to ? = 3? ? 4, you know the new slope will be 3
Perpendicular Lines ¡ö Lines are considered perpendicular when they cross one another at a 90? angle. ¡ö Algebraically, if one line has a slope of ?, a line perpendicular to it will have a slope of ? 1 ? . (Opposite reciprocal) ¡ö The green line in the picture has a slope of 2 3 . The blue line, which is perpendicular to it, has a slope of ? 3 2 .
Equation Example 3 Since parallel lines have the same slope, we need to find the slope of the given line. ¡ö 6x + 2y = 32 ¡ö 2y = ?6x + 32 ¡ö y = ?3x + 16 ¡ö ? = ?3 Find the equation of the line parallel to the line 6? + 2? = 32 and goes through the point (2,7). Now we can find the equation. ¡ö y ? 7 = ?3(x ? 2) ¡ö y ? 7 = ?3x + 6 ¡ö y = ?3x + 13
Your Turn Find the equation of the line perpendicular to the line 2? + 4? = 16 and goes through the point (2,7). Find the equation of the line that passes through the points (?3,7) and 5, ?9 .
UPCOMING EVENTS ¡ö Tackle the Math Series ¨C Why Does Order Matter? ¨C 4 Out of 3 People Struggle with Math ¨C Probably Probability ¨C Do You Know the Line? ¨C Beating the System (of Equations)
Our Services Study Help ? Drop-In Study Help for all courses ? Study Groups ? On-Track Appointments ? Question Drop-Off Tech Help ? Drop-In Student Tech Help ? Ask-a-Lab Associate Question Drop-off ? Get Tech Ready and Appy Hour Workshops Learning Help ? Check out our collection of self-service resources that supplement classroom materials Get In Touch! www.wccnet.edu/LC (live chat assistance offered during regular hours) (734) 973-3420 Lab Email: LCLab@wccnet.edu Tutoring Email: TutorWCC@wccnet.edu

More Related Content

Do you know the line

  • 1. DO YOU KNOW THE LINE? Tackle the Math All Things Lines
  • 2. Example of Linear Equation ¡ö Linear equations are always straight lines when graphed. ¡ö They always fit the following formulas: ¨C Slope-intercept form: ? = ?? + ?, where m is the slope and b is the y-intercept. ¨C Point-slope form: ? ? ?1 = ?(? ? ?1), where m is the slope and ?1, ?1 is a point. ¨C General form: ?? + ?? = ? ¡ö Slope-intercept form and point-slope form are by far the most common.
  • 3. Slope ¡ö The ¡°slope¡± of a line is the measure of its steepness. ¡ö Other terms for slope are average rate of change and rise over run ¡ö The equation for slope is as follows: ¨C ? = ?2??1 ?2??1 ¨C To find the slope, you must have two points ?1, ?1 ??? ?2, ?2 .
  • 4. Slope Example Find the slope of a line with points (1, 3) and (4, 12). ¡ö First, determine ?1, ?1 ??? ?2, ?2 . ¡ö ?1 = 1, ?1 = 3, ?2 = 4, ??? ?2 = 12. ¡ö Now let¡¯s use the slope equation. ¡ö ? = ?2??1 ?2??1 ¡ö ? = 12?3 4?1 ¡ö ? = 9 3 ¡ö ? = 3
  • 5. Equation Example Find the equation of a line which has a slope of 2 and goes through the point (1, 5). ¡ö Since we already know the slope, it would be prudent to use slope-intercept form: ? = ?? + ?. m = 2.We do not, however, know the y-intercept (b).This is not a problem.We can replace m, x, and y with the slope and point given. ¡ö ? = ?? + ? ¡ö 5 = 2 1 + ?. Now we solve for b. ¡ö 5 = 2 + ? ¡ö 3 = ?. Now we have everything we need! Let¡¯s plug in m and b to slope-intercept form. ¡ö ? = 2? + 3
  • 6. Equation Example 2 ¡ö ? = 8?0 2?(?2) = 8 4 = 2 ¡ö ? = 2? + ? ¡ö 0 = 2 ?2 + ? ¡ö 0 = ?4 + ? ¡ö 4 = ? ¡ö ? = 2? + 4 Find the equation of the line passing through the points (-2, 0) and (2, 8). Slope-Intercept ? = ?? + ? Point-Slope ? ? ?1 = ? ? ? ?1 ¡ö ? = 8?0 2?(?2) = 8 4 = 2 ¡ö ? ? ?1 = 2 ? ? ?1 ¡ö ? ? 8 = 2 ? ? 2 ¡ö ? ? 8 = 2? ? 4 ¡ö ? = 2? + 4
  • 7. Parallel Lines ¡ö Lines are considered parallel when they never touch. ¡ö Algebraically, they have the same slope. ¡ö If you¡¯re given a problem which says, ¡°Find the equation of a line passing through the point (1, 2) and parallel to ? = 3? ? 4, you know the new slope will be 3
  • 8. Perpendicular Lines ¡ö Lines are considered perpendicular when they cross one another at a 90? angle. ¡ö Algebraically, if one line has a slope of ?, a line perpendicular to it will have a slope of ? 1 ? . (Opposite reciprocal) ¡ö The green line in the picture has a slope of 2 3 . The blue line, which is perpendicular to it, has a slope of ? 3 2 .
  • 9. Equation Example 3 Since parallel lines have the same slope, we need to find the slope of the given line. ¡ö 6x + 2y = 32 ¡ö 2y = ?6x + 32 ¡ö y = ?3x + 16 ¡ö ? = ?3 Find the equation of the line parallel to the line 6? + 2? = 32 and goes through the point (2,7). Now we can find the equation. ¡ö y ? 7 = ?3(x ? 2) ¡ö y ? 7 = ?3x + 6 ¡ö y = ?3x + 13
  • 10. Your Turn Find the equation of the line perpendicular to the line 2? + 4? = 16 and goes through the point (2,7). Find the equation of the line that passes through the points (?3,7) and 5, ?9 .
  • 11. UPCOMING EVENTS ¡ö Tackle the Math Series ¨C Why Does Order Matter? ¨C 4 Out of 3 People Struggle with Math ¨C Probably Probability ¨C Do You Know the Line? ¨C Beating the System (of Equations)
  • 12. Our Services Study Help ? Drop-In Study Help for all courses ? Study Groups ? On-Track Appointments ? Question Drop-Off Tech Help ? Drop-In Student Tech Help ? Ask-a-Lab Associate Question Drop-off ? Get Tech Ready and Appy Hour Workshops Learning Help ? Check out our collection of self-service resources that supplement classroom materials Get In Touch! www.wccnet.edu/LC (live chat assistance offered during regular hours) (734) 973-3420 Lab Email: LCLab@wccnet.edu Tutoring Email: TutorWCC@wccnet.edu