202k views
3 votes
Which equations represent the line that is perpendicular to the line 5x – 2y = -6 and passes through the point (5, -4)? Select three options.

a) y = -2/5x - 2
b) 2x + 5y = -10
c) 2x - 5y = -10
d) y + 4 = -2/5(x - 5)
e) Dy - 4 = 5/2(x + 5)

User Mina Wissa
by
8.6k points

1 Answer

3 votes

Final answer:

Equations representing a line perpendicular to the line 5x – 2y = -6 and passing through (5, -4) can be derived using the negative reciprocal slope of -2/5 and the point-slope form, yielding options (b) 2x + 5y = -10 and (d) y + 4 = -2/5(x - 5). Option (c) is not a valid equation as it does not represent the perpendicular line passing through (5, -4).

Step-by-step explanation:

The question asks for equations that represent a line perpendicular to the line 5x – 2y = -6 and passes through the point (5, -4). First, we find the slope of the given line by rewriting the equation in slope-intercept form: y = mx + b. For 5x – 2y = -6, dividing every term by -2 gives us y = (5/2)x + 3. Thus, the slope is 5/2. A line perpendicular to this would have a negative reciprocal slope which is -2/5. Now, using the point (5, -4) and the slope -2/5, we apply the point-slope form of the equation, y - y1 = m(x - x1), which gives us y + 4 = -2/5(x - 5), matching option (d).

To find a standard form equation like option (b) and (c), we can rearrange (d) and multiply by 5 to eliminate fractions, giving us 5y + 20 = -2x + 10, leading to 2x + 5y = -10, which corresponds to option (b). Note that option (c) is not equivalent as its rearrangement does not pass through the point (5, -4). Lastly, option (a) differs in slope and thus is not perpendicular, while option (e) contains a typographical error with 'D' instead of 'y', disqualifying it as well.

User Joostschouten
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.