Podcast
Questions and Answers
What information is required to write an equation in point-slope form?
What information is required to write an equation in point-slope form?
- Two points on the line
- The x and y intercepts
- A point on the line and the slope (correct)
- The slope of the line and the y-intercept
The point-slope form of a linear equation can only be used for lines with a positive slope.
The point-slope form of a linear equation can only be used for lines with a positive slope.
False (B)
Write the point-slope form equation of a line that passes through the point (5, -3) and has a slope of -2.
Write the point-slope form equation of a line that passes through the point (5, -3) and has a slope of -2.
y+3=-2(x-5)
In the point-slope form equation $y - y_1 = m(x - x_1)$, 'm' represents the ______ of the line.
In the point-slope form equation $y - y_1 = m(x - x_1)$, 'm' represents the ______ of the line.
Given a line with the equation $y - 2 = 3(x + 1)$, what is the slope of the line?
Given a line with the equation $y - 2 = 3(x + 1)$, what is the slope of the line?
If two lines have the same slope, they are always parallel.
If two lines have the same slope, they are always parallel.
A line passes through the point (-1, 4) and is parallel to a line with a slope of 2. What is the slope of the line?
A line passes through the point (-1, 4) and is parallel to a line with a slope of 2. What is the slope of the line?
The point-slope form is particularly useful when you know a point on a line and its ______.
The point-slope form is particularly useful when you know a point on a line and its ______.
Match the point-slope equations with the corresponding point and slope:
Match the point-slope equations with the corresponding point and slope:
Which equation represents a line passing through the point (4, -1) with a slope of -3?
Which equation represents a line passing through the point (4, -1) with a slope of -3?
Flashcards
Point-Slope Form
Point-Slope Form
y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Slope (m)
Slope (m)
A straight line's steepness and direction.
Point (x₁, y₁)
Point (x₁, y₁)
A location on a coordinate plane, designated (x, y).
When to Use Point-Slope Form
When to Use Point-Slope Form
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How to Use Point-Slope Form
How to Use Point-Slope Form
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Study Notes
- An equation can be written in point-slope form when given a point and a slope.
Point-Slope Formula
- y - y₁ = m(x - x₁)
- m represents the slope
- (x₁, y₁) is a point the line passes through
Example
- Equation of a line passing through (2, -4) with a slope of ²/₃ should first be written in point-slope formula: y - y₁ = m(x - x₁)
- Then substitute (2, -4) for (x₁, y₁) and ²/₃ for m
- y - (-4) = ²/₃(x - 2) simplifies to y + 4 = ²/₃(x - 2)
Your Turn
- For the values (3, 5) and m = 6, first write the point-slope formula: y - y₁ = m(x - x₁)
- y - 5 = 6(x - 3)
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