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Questions and Answers
What is the main purpose of converting point-slope form to slope-intercept form?
What is the main purpose of converting point-slope form to slope-intercept form?
- To easily identify the slope and y-intercept of the line. (correct)
- To express the line in terms of its x-intercept.
- To calculate the distance between two points on the line.
- To determine the vertical asymptote of the line.
Which of the following correctly represents point-slope form of a linear equation?
Which of the following correctly represents point-slope form of a linear equation?
- $y - y_1 = rac{1}{m}(x - x_1)$
- $y - y_1 = m(x - x_1)$ (correct)
- $y = mx + b$
- $y = rac{b}{x} + m$
What is the relationship between the point-slope form and slope-intercept form of a linear equation?
What is the relationship between the point-slope form and slope-intercept form of a linear equation?
- Slope-intercept form is a subset of point-slope form.
- Point-slope form can only be used for horizontal lines.
- They are completely unrelated forms.
- They have the same mathematical implications but differ in structure. (correct)
If a line has a slope of 2 and passes through the point (3, 4), what is its equation in point-slope form?
If a line has a slope of 2 and passes through the point (3, 4), what is its equation in point-slope form?
When converting from point-slope form to slope-intercept form, what is the first step you should take?
When converting from point-slope form to slope-intercept form, what is the first step you should take?
Flashcards
Point-Slope Form
Point-Slope Form
An equation of a line given a point on the line and the slope of the line.
Slope-Intercept Form
Slope-Intercept Form
An equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
Converting Point-Slope to Slope-Intercept
Converting Point-Slope to Slope-Intercept
Transforming an equation in point-slope form into slope-intercept form.
Equation of a line
Equation of a line
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Study Notes
Converting Point-Slope Form to Slope-Intercept Form
- Point-slope form of a linear equation is y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a point on the line.
- Slope-intercept form is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
- To convert from point-slope to slope-intercept form, simplify the point-slope equation until it resembles the slope-intercept form.
Steps for Conversion
- Distribute: Distribute the slope 'm' to the terms inside the parentheses in the point-slope equation.
- Simplify: Simplify both sides of the equation by combining like terms and solving for 'y'.
- Isolate 'y': Ensure the equation is solved for 'y' (i.e., y = ...), which is the structure of the slope-intercept form.
- Identify the slope: The coefficient of 'x' will be the slope.
- Identify the y-intercept: The constant term in the equation is the y-intercept.
Example
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Consider the point-slope form: y - 2 = 3(x - 1)
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Distribute: y - 2 = 3x - 3
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Simplify: y = 3x - 1
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This results in the slope-intercept form: y = 3x - 1
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The slope is 3, and the y-intercept is -1.
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