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# Equations of Lines

## 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.

#### 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.

#### 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.

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.

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.
1. Write an equation of the line that passes through P(-1,1) and is perpendicular to the line y=7/3x+10.

### 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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