Final answer:
To find the parallel line's equation, convert the original line to slope-intercept form to find its slope, then use the y-intercept from the second line. The final equation is y = 2x - 5.
Step-by-step explanation:
To find the equation of a line that is parallel to −8x−4y=1 and shares the same y-intercept as 4x+6y=−30, we need to carry out a couple of steps. First, we determine the slope of the original line by rewriting it in slope-intercept form (y = mx + b), where m represents the slope. For −8x−4y=1, dividing each term by −4 will give us y = 2x + 0.25. Therefore, the slope of the parallel line should also be 2.
Next, we find the y-intercept of the second line by rewriting 4x+6y=−30 in the slope-intercept form. Dividing each term by 6 gives us y = −(2/3)x − 5. Hence, the y-intercept is −5. Now, we can write the equation of the parallel line with a slope of 2 and a y-intercept of −5. The equation is y = 2x − 5.