How Do You Solve a Linear Algebra Slope Problem?

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SUMMARY

The discussion focuses on solving a linear algebra problem involving the equation of a line and finding the distance from a point to that line. The equation provided is 6y + 3x = 3, which can be rearranged to find the slope, m. The slope of the perpendicular line is determined using the formula -1/m. The solution involves finding the intersection of the two lines and calculating the distance from the point (8, -1) to this intersection point.

PREREQUISITES
  • Understanding of linear equations and slope-intercept form
  • Knowledge of perpendicular lines and their slopes
  • Ability to solve simultaneous equations
  • Familiarity with distance formulas in coordinate geometry
NEXT STEPS
  • Learn how to convert standard form equations to slope-intercept form
  • Study the properties of perpendicular lines in geometry
  • Practice solving simultaneous linear equations
  • Explore the distance formula between a point and a line
USEFUL FOR

Students studying algebra, particularly those tackling linear equations and geometry, as well as educators looking for examples of distance calculations in coordinate systems.

DethRose
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Hey i have a homework assignment due and have no idea how to answer 1 of the questions

the question is

Find m and recal m perpendicular = -1/m. Also sketch the situation showing what the required distance is.

6y+3x=3 ; (8,-1)

all assistance is much appreciated

thanks
 
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I think you need to find the distance between the point and the line. The distance is a line coming out of the point and is perpendicular to the first line.
 
1) To find the slope, m, of 6y+ 3x= 8, solve for y: the equation will be in the form y= mx+ b.

2) Of course, any line perpendicular to that line will have slope
-1/m. What is the equation of a line through (8,-1) with slope
-1/m? (Use the value of m you found in 1).)

3) Where do those two lines cross? Solve the two equations simultaneously.

4. What is the distance from (8, -1) to the point you found in 3)?
 

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