Final answer:
To put the equation -2x = 2y + 4 into slope-intercept form, subtract 2y from both sides, giving us -2x - 2y = 4. Divide both sides by -2 to isolate y, resulting in y = -x - 2. The slope is -1 and the y-intercept is -2. The x-intercept is (-2, 0). The domain and range are all real numbers.
Step-by-step explanation:
To put the equation -2x = 2y + 4 into slope-intercept form, we need to isolate y on one side of the equation. First, let's subtract 2y from both sides, giving us -2x - 2y = 4. We can rewrite this as -2y = 2x + 4. Then, divide both sides by -2 to isolate y, resulting in y = -x - 2. Now we have the equation in slope-intercept form, y = mx + b, where m is the slope (-1 in this case) and b is the y-intercept (-2 in this case).
To construct the graph, we can start by plotting the y-intercept, which is -2. From there, we can use the slope to find additional points on the line. Since the slope is -1, we can go up 1 unit and right 1 unit, or down 1 unit and left 1 unit, to find more points. Connecting these points will give us the graph of the equation.
The x-intercept is the point where the line crosses the x-axis, and it occurs when y = 0. Plugging in y = 0 into our equation, we get 0 = -x - 2. Solve for x, and we find that the x-intercept is -2. Therefore, the x-intercept is (-2, 0).
The domain of this equation is all real numbers, because there are no restrictions on the values of x.
The range of this equation is all real numbers, because the line extends infinitely in both the upward and downward directions.
Learn more about Slope-intercept form of equations