Final answer:
The equation for the line that is perpendicular to the line 9x-4y=-4 and has the same y-intercept as -6x-8y=2 is y = (-4/9)x - 1/4.
Step-by-step explanation:
The subject of this question is finding the equation of a line that is perpendicular to a given line and that has the same y-intercept as another provided line. To determine the equation of our desired line, we first need to find the slopes of the given lines and then use the concept that perpendicular lines have slopes that are negative reciprocals of each other.
The first step is to rewrite the given equations 9x-4y=-4 and -6x-8y=2 in slope-intercept form (y = mx + b), where 'm' represents the slope, and 'b' the y-intercept. The equation 9x-4y=-4 can be rewritten as y = (9/4)x + 1, giving us a slope of 9/4. Since we want a line perpendicular to this, our desired slope must be the negative reciprocal, which is -4/9.
The y-intercept is found from the second equation -6x-8y=2. We rewrite it in slope-intercept form as y = (3/4)x - 1/4. The y-intercept here is -1/4, which is the same y-intercept we want for our new line. Therefore, the equation for the line perpendicular to the line 9x-4y=-4 with the same y-intercept as -6x-8y=2 is y = (-4/9)x - 1/4.
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