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
- 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?
- Graph the equation: 2x – 3y =6
- Write an equation of the line that passes through (-2,5) and (1,2)
- Write an equation of the line shown.
- Write an equation of the line that passes through P(-1,1) and is perpendicular to the line y=7/3x+10.
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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