Find an equation of a line perpendicular to the given line and contains the given point. Write t

step 1 this is a problem number 475 okay now we have line 4x minus 3y equal to 5 and we need to find th

Find an equation of a line perpendicular to the given line...

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Key Concepts

Conversion from Standard Form to Slope-Intercept Form

Many linear equations start in standard form, expressed as Ax + By = C. Converting this to the slope-intercept form (y = mx + b) involves solving for y, which makes it easier to identify the slope and the y-intercept for further manipulation or graphing purposes.

Point-Slope Form

The point-slope form of a line, given by the equation y - y1 = m(x - x1), is used to construct the equation of a line when a point on the line (x1, y1) and the slope m are known. This form is particularly helpful when building an equation based on specific point and slope information.

Slope-Intercept Form

This is a method of expressing the equation of a line in the form y = mx + b, where m represents the slope and b is the y-intercept. It allows for a straightforward identification of the line's steepness and where it crosses the y-axis, which is useful for graphing and analysis.

Perpendicular Lines

Perpendicular lines intersect at a right angle (90°). In terms of slopes, this means that the slopes of two perpendicular lines are negative reciprocals of each other. If one line has a slope m, then a line perpendicular to it will have a slope of -1/m.

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