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Equations of Lines

Sep 12, 2022
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Key Concepts

  • Slope-intercept form of general form of linear equation.
  • Equation of a line from a graph.
  • Equation of a parallel line.
  • Equation of a perpendicular line.
  • Equation to relate real-world problems
  • Graph of a line with equation in standard form.

Equations of Lines

1. Intercepts of a line 

The point where the graph crosses the x− axis is called the 𝒙 intercept of the graph. 

The point where the graph crosses the y− axis is called the 𝒚 intercept of the graph. 

Intercepts of a line Equations of Lines:

2. Slope-intercept form of a linear equation of a line 

Linear equations may be written in different forms. The general form of a linear equation in slope-intercept form is y = mx+b where m is the slope of the line and b is the y-intercept of the line. 

Slope-intercept form of a linear equation of a line 

3. Write an equation of a parallel line 

To write the equation of a line parallel to a given line and passing through a point: 

Step 1: Find the slope of the given line. 

parallel

Slope of parallel lines is equal. 

Step 2: Find the y− intercept by substituting the slope and given point in slope-intercept form. 

4. Write an equation of a perpendicular line 

To write the equation of a line perpendicular to a given line and passing through a point: 

Step 1: Find the slope of the given line. 

Find the slope of the required line. 

parallel

Since the product of slopes perpendicular lines is −1

Step 2: Find the y− intercept by substituting the slope and given point in slope-intercept form. 

5. Write an equation in standard form 

The equation of a line is written in standard form as Ax + By = C where A and B are not equal to zero. 

6. Write an equation to relate real-world problems 

We can write linear equations to model real-world situations, such as 

  • To compare costs. 
  • To solve age-related problems. 
  • To solve work, time, and wages problems. 
  • To calculate the speed, distance, and time of a moving object. 

Exercise

  1. The equation y=50x+125 models the total cost of joining a climbing gym. What is the meaning of the slope and the y-intercept of the line?
  2. Graph the equation: 2x – 3y =6
  3. Write an equation of the line that passes through (-2,5) and (1,2)
  4. Write an equation of the line shown.
exercise
  1. Write an equation of the line that passes through P(-1,1) and is perpendicular to the line y=7/3x+10.

Concept Map 

Concept Map: 

What we have learned

  • The general form of a linear equation in slope-intercept form is y=mx+b where m is the slope of the line and b is the y-intercept of the line.
  • The equation of a line is written in standard form as Ax+By=C where A and B are not equal to zero.
  • We can write an equation to relate real-world problems.

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