Understanding Point-Slope Form in Algebra 1
Point-slope form is a fundamental concept in Algebra 1, used to represent the equation of a line in a specific format. The point-slope form is given by the equation y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
How to Write the Equation of a Line in Point-Slope Form
To write the equation of a line in point-slope form, follow these steps:
- Identify the slope (m) of the line
- Identify a point (x1, y1) on the line
- Plug in the values of m, x1, and y1 into the point-slope form equation: y - y1 = m(x - x1)
Example 1: Writing the Equation of a Line in Point-Slope Form
Find the equation of the line with a slope of 2 and passing through the point (3, 4).
- m = 2
- (x1, y1) = (3, 4)
- Plug in the values into the point-slope form equation: y - 4 = 2(x - 3)
Example 2: Writing the Equation of a Line in Point-Slope Form
Find the equation of the line with a slope of -3 and passing through the point (-2, 5).
- m = -3
- (x1, y1) = (-2, 5)
- Plug in the values into the point-slope form equation: y - 5 = -3(x + 2)
Worksheet Answer Key
Here is the answer key for the point-slope form worksheet:
| Problem | Answer |
|---|---|
| 1. Find the equation of the line with a slope of 4 and passing through the point (2, 3). | y - 3 = 4(x - 2) |
| 2. Find the equation of the line with a slope of -2 and passing through the point (5, 1). | y - 1 = -2(x - 5) |
| 3. Find the equation of the line with a slope of 3 and passing through the point (-1, 2). | y - 2 = 3(x + 1) |
| 4. Find the equation of the line with a slope of -5 and passing through the point (4, 2). | y - 2 = -5(x - 4) |
📝 Note: Make sure to plug in the correct values for m, x1, and y1 into the point-slope form equation to get the correct answer.
In conclusion, understanding point-slope form is a crucial concept in Algebra 1. By following the steps outlined above and practicing with the worksheet, you should be able to write the equation of a line in point-slope form with ease.
What is the point-slope form of a linear equation?
+The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line.
How do I find the slope of a line?
+The slope of a line can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Can I use point-slope form to find the equation of a line if I only know the slope and the y-intercept?
+No, point-slope form requires a point on the line and the slope. If you only know the slope and the y-intercept, you can use the slope-intercept form (y = mx + b) to find the equation of the line.
Related Terms:
- Point slope form Worksheet Kuta
- Graphing point-slope form worksheet
- Algebra 1 point-slope form worksheet
- Graphing point-slope form worksheet PDF
- Point-slope form Notes
