Use the given conditions to write an equation for each line...

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form.
Passing through $(-4,2)$ and perpendicular to the line whose equation is $y=\frac{1}{3} x+7$

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Key Concepts

Perpendicular Lines

In the context of linear equations, perpendicular lines have slopes that are negative reciprocals of each other. This means if one line has a slope of m, then the line perpendicular to it will have a slope of -1/m. This property is crucial when determining the equation of a line that must be perpendicular to a given line.

Slope-Intercept Form

The slope-intercept form of a line is a way to express the line's equation using its slope and y-intercept. It is written as y = mx + b, where m represents the slope and b represents the y-intercept. This form makes it easy to graph the line and understand how it intercepts the y-axis.

Equation of a Line

An equation of a line is a mathematical expression that represents all the points lying on the line. It typically involves a relationship between x and y coordinates and can be expressed in multiple forms depending on which characteristics of the line (such as slope, y-intercept, or a specific point) are most useful for a given problem.

Point-Slope Form

The point-slope form of a line is used when a specific point on the line and the slope are known. It is generally written as (y - y?) = m(x - x?), where (x?, y?) is a point on the line and m is its slope. This form is particularly useful for quickly setting up an equation from given information.

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