Final answer:
The equation of a line parallel to 6x + 2y = -3 and passing through the point (2,-5) is y = -3x + 1.
Step-by-step explanation:
To find the equation of a line that is parallel to the line 6x + 2y = -3 and passes through the point (2,-5), we need to determine the slope of the given line. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The slope of the given line can be found by rearranging the equation to solve for y and then comparing it to the standard form y = mx + b.
- Rearrange the equation 6x + 2y = -3 to solve for y: 2y = -6x - 3 ---> y = -3x - 3/2
- Compare the equation to the slope-intercept form y = mx + b and we can see that the slope is -3
- Since we want a line parallel to the given line, the slope of the parallel line will also be -3
- Now we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is y - y1 = m(x - x1) where (x1,y1) is the given point. Plugging in the values, we get: y - (-5) = -3(x - 2) ---> y + 5 = -3x + 6
- Rearrange the equation to solve for y: y = -3x + 1
Therefore, the equation of a line parallel to 6x + 2y = -3 and passes through the point (2,-5) is y = -3x + 1.