Final answer:
To find the equation of a line that is parallel to -2x+4y=8, we need to determine the slope of the given line and the y-intercept. By rearranging the equation into slope-intercept form, we find that the slope is 1/2. Using the point (-5, -1) and the slope, we can find the y-intercept and the equation of the parallel line, which is y = (1/2)x + 9/2.
Step-by-step explanation:
To find the equation of a line that is parallel to the line -2x+4y=8, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept. To determine the slope of the given line, we need to rearrange the equation into slope-intercept form.
In this case, we have -2x+4y=8. By isolating y in terms of x, we get y = (2x + 8)/4, which simplifies to y = (1/2)x + 2. Thus, the slope of the given line is 1/2. Since we want to find a line that is parallel to this line, the parallel line will also have a slope of 1/2. Therefore, the equation of the parallel line passing through the point (-5, -1) is y = (1/2)x + b, where b is the y-intercept we need to find.