Find an equation of the line that passes through the given point and is perpendicular to the giv

step 1 So on this example, I want to write the equation in slope intercept form that passes through thi

Find an equation of the line that passes through the given...

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Key Concepts

Point-Slope Form

A useful equation form to represent a line when a specific point and the slope are known. It is expressed as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form can easily be rearranged to obtain the slope-intercept form.

Perpendicular Lines

In the context of coordinate geometry, two lines are perpendicular if they meet at a 90-degree angle. A key property of perpendicular lines is that their slopes are negative reciprocals of each other, meaning if one line has a slope m, the other will have a slope of -1/m, assuming neither line is vertical.

Slope of a Line

The slope is a measure of the steepness and direction of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It indicates how much the y-coordinate changes for a unit change in the x-coordinate.

Slope-Intercept Form

A method to express the equation of a line in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form makes it easy to understand the line's gradient and where it cuts the y-axis.

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