Answer:
y= -5x + 21
Step-by-step explanation:
The equation of the line that passes through (5, -4) and is perpendicular to line y = 1/5x + 4 is y= -5x + 21
The slope that is perpendicular to the slope 1/5x is -5x.
To find a perpendicular slope, you take the negative reciprocal. (so you change the signs (1/5x is positive so now it would be negative) and -5/1 is basically -5)
However, y = -5x + 4 does NOT pass through (5, -4)
But we still have to write the equation in slope intercept form or the equation of the line
<em>The formula for slope- intercept form is : y= mx + b</em>
<em>So we must plug in (m) which is our -5x and for y we look at the coordinates they gave us ----- (5, -4). -4 is our y. In the coordinates we also have x listed which is 5, so we all plug that in. </em>
<em>y = -5x + b (as you can see -5x is plugged in here)</em>
<em>-4 = -5x + b (as you can see -4 is plugged in here)</em>
<em>4 = -5(5) + b (as you can see 5 is plugged in here)</em>
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<em>NOW WE MUST SOLVE!</em>
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<h3><em>Isolate B</em></h3>
<em>-4 = -25 + b</em>
Add 25 from both sides.
<em>-4 = -25 + b</em>
+25 25
<em>----------------</em>
<em>21 = b</em>
We can now plug this into our slope intercept formula---y= mx+ b---to find the equation of the line.
<h2>
Therefore, y = -5 x +21</h2>
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