SOLUTION: write the slope -int form for an equation of a line that passes through (0,4) and is perpendicular to the graph 3x+ 8y=4

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Question 253953: write the slope -int form for an equation of a line that passes through (0,4) and is perpendicular to the graph 3x+ 8y=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B8y=4 Start with the given equation.


8y=4-3x Subtract 3x from both sides.


8y=-3x%2B4 Rearrange the terms.


y=%28-3x%2B4%29%2F%288%29 Divide both sides by 8 to isolate y.


y=%28%28-3%29%2F%288%29%29x%2B%284%29%2F%288%29 Break up the fraction.


y=-%283%2F8%29x%2B1%2F2 Reduce.


We can see that the equation y=-%283%2F8%29x%2B1%2F2 has a slope m=-3%2F8 and a y-intercept b=1%2F2.


Now to find the slope of the perpendicular line, simply flip the slope m=-3%2F8 to get m=-8%2F3. Now change the sign to get m=8%2F3. So the perpendicular slope is m=8%2F3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=8%2F3 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-4=%288%2F3%29%28x-0%29 Plug in m=8%2F3, x%5B1%5D=0, and y%5B1%5D=4


y-4=%288%2F3%29x%2B%288%2F3%29%280%29 Distribute


y-4=%288%2F3%29x%2B0 Multiply


y=%288%2F3%29x%2B0%2B4 Add 4 to both sides.


y=%288%2F3%29x%2B4 Combine like terms.


So the equation of the line perpendicular to 3x%2B8y=4 that goes through the point is y=%288%2F3%29x%2B4.


Here's a graph to visually verify our answer:


Graph of the original equation y=-%283%2F8%29x%2B1%2F2 (red) and the perpendicular line y=%288%2F3%29x%2B4 (green) through the point .