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 for each step in your final answer. Type your answer in the box provided to submit your solution.
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
a) The standard form of the equation is Ax + By = C.
b) To determine the slope of the line, we need to rearrange the given equation 2x + y = -5 into slope-intercept form, y = mx + b, where m is the slope. Subtract 2x from both sides of the equation:
y = -2x - 5
The coefficient of x is -2, so the slope of the line is -2.
c) The point-slope form of the line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The y-intercept of the line is (0, 2), so the point-slope form becomes:
y - 2 = -2(x - 0)
y - 2 = -2x
d) To rearrange the equation into standard form, we distribute the -2:
y - 2 = -2x
2x + y = 2
Rearranging the terms:
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.