Question

What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply.

A) y = −x − 1
B) 2x + 5y = −5
C) y = −x − 3
D) 2x + 5y = −15
E) y − 1= −(x + 5)

Answer 1

The equation of the line parallel to 2x + 5y = 10 and passing through the point (–5, 1) is 2x + 5y = -5. This is found by first determining the slope of the given line and then using the point-slope form to find the equation passing through the given point.

Step-by-step explanation:

The question asks for the equation of a line that is parallel to the given line 2x + 5y = 10 and that passes through the point (–5, 1). To find this, we first need to determine the slope of the given line by putting it in slope-intercept form (y = mx + b), where m represents the slope. Rearranging 2x + 5y = 10 into y = -2/5x + 2, we find that the slope (m) is -2/5. The new line must have the same slope since it is parallel. Using the point-slope form of a line (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point, we have:

• y - 1 = -2/5(x + 5)
• y - 1 = -2/5x - 2
• y = -2/5x - 1

Multiplying through by 5 to eliminate the fraction:

• 5y = -2x - 5
• 2x + 5y = -5

Therefore, the correct equation of the line parallel to 2x + 5y = 10 and passing through the point (–5, 1) is 2x + 5y = -5, which corresponds to option B.