Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 2, passing through (3, 5)

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Recall the point-slope form of a line equation: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.

Substitute the given slope \(m = 2\) and the point \((3, 5)\) into the point-slope form: \(y - 5 = 2(x - 3)\).

To convert to slope-intercept form, start by distributing the slope on the right side: \(y - 5 = 2x - 6\).

Next, isolate \(y\) by adding 5 to both sides: \(y = 2x - 6 + 5\).

Simplify the right side to get the slope-intercept form: \(y = 2x - 1\).

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주요 개념

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Point-Slope Form of a Line

The point-slope form is an equation of a line expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. It is useful for writing the equation when you know a point and the slope.

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This form clearly shows the slope and where the line crosses the y-axis, making it easy to graph and interpret.

Using Given Conditions to Find the Equation

Given a slope and a point, you substitute these values into the point-slope form to write the equation. Then, by simplifying and solving for y, you convert it into slope-intercept form, revealing the y-intercept.