Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work in your final answer. Type your answer in the box provided submit your solution.
To find the equation of the line that is parallel to 2x + y = -5, we need to determine the slope of the given line and use it to write the equation of the new line.
First, let's convert the given equation to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Rearranging the equation, we have y = -2x - 5.
From this equation, we can see that the slope of the given line is -2.
Since the line we want to find is parallel to the given line, it will have the same slope of -2.
Now, we can write the equation of the new line.
In slope-intercept form, the equation is y = mx + b, where m is the slope and b is the y-intercept.
We know that the y-intercept is 2, so b = 2. The slope is -2, so m = -2.
The equation of the line is y = -2x + 2.
To convert this equation to standard form Ax + By = C, we multiply through by -1:
-1 * y = -1 * (-2x + 2)
-y = 2x - 2
Now, we move all the terms to one side of the equation:
2x + y = -2
Therefore, the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5 is 2x + y = -2.