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Converting Point-Slope to Slope-Intercept Form

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Converting Point-Slope to Slope-Intercept Form

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Questions and Answers

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?

$y - y_1 = rac{1}{m}(x - x_1)$

$y - y_1 = m(x - x_1)$ (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?

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?

<p>$y - 4 = 2(x - 3)$</p> Signup and view all the answers

When converting from point-slope form to slope-intercept form, what is the first step you should take?

<p>Isolate $y$ on one side of the equation.</p> Signup and view all the answers

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

Consider the point-slope form: y - 2 = 3(x - 1)
Distribute: y - 2 = 3x - 3
Simplify: y = 3x - 1
This results in the slope-intercept form: y = 3x - 1
The slope is 3, and the y-intercept is -1.

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Description

This quiz focuses on the conversion of linear equations from point-slope form to slope-intercept form. You will learn the steps involved in simplifying the point-slope equation and isolating 'y'. Test your understanding through practical examples.