Write an equation of the line satisfying the given...

Write an equation of the line satisfying the given conditions. Give the final answer in slope-intercept form. (Hint: Recall the relationships among slopes of parallel and perpendicular lines.) Passes through (4,2) perpendicular to $x-3 y=7$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Slope-Intercept Form

The slope-intercept form is an equation of a line written as y = mx + b, where m represents the line's slope and b represents the y-intercept. This form is particularly useful for quickly identifying the rate of change and where the line crosses the y-axis.

Point-Slope Form

The point-slope form, given by y - y? = m(x - x?), is used to write the equation of a line when a point (x?, y?) on the line and the slope m are known. It is a versatile formulation that can then be manipulated into other forms, such as the slope-intercept form.

Slope from Standard Form

When a line is given in standard form, Ax + By = C, the slope of the line can be found by rewriting it into the slope-intercept form or by using the formula m = -A/B directly. This conversion is necessary when the line's equation is provided in a form that does not make the slope immediately apparent.

Perpendicular Lines

Perpendicular lines are lines that intersect at a right angle. The key property of their slopes is that the product of the slopes of two perpendicular lines is -1, meaning if one line has slope m, the line perpendicular to it has slope -1/m. This relationship is crucial when tasked with finding the equation of a line that is perpendicular to another.

Transcript

Please give Ace some feedback