190k views
5 votes
Which equation represents the line that is parallel to 5x + y = 13 and passes through the point (15, -31)?

User Fumie
by
7.4k points

1 Answer

6 votes

Final answer:

The equation of a line parallel to 5x + y = 13 that passes through the point (15, -31) has the same slope as the given line, which is -5. Using the point-slope form, the equation of the line is found to be y = -5x + 44.

Step-by-step explanation:

The equation of a line that is parallel to another can be found by ensuring that the two lines have the same slope. To find an equation of a line that is parallel to 5x + y = 13 and passes through the point (15, -31), firstly, we need to write the given equation in slope-intercept form to identify the slope. Starting with 5x + y = 13, we can subtract 5x from both sides to get y = -5x + 13, so the slope (m) is -5.

Since parallel lines have equal slopes, the new line will also have a slope of -5. Now, using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can plug in the known values. Substituting -31 for y1, 15 for x1, and -5 for m gives us y - (-31) = -5(x - 15). Simplifying this, we find y + 31 = -5x + 75.

To put it into slope-intercept form, we subtract 31 from both sides to find the final equation y = -5x + 44. Therefore, the equation of the line parallel to 5x + y = 13 and passing through the point (15, -31) is y = -5x + 44.

User Randak
by
9.0k points

No related questions found

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

9.4m questions

12.2m answers

Categories