Answer:
Explanation:
We can find the slope of this line by rearranging it into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
5x - 3y = 8 -3y = -5x + 8 y = (5/3)x - (8/3)
So the slope of the line 5x - 3y = 8 is 5/3.
The line perpendicular to this line will have a slope that is the negative reciprocal of 5/3. That means the slope of the new line is -3/5.
Now we can use the point-slope form of the equation of a line to find the equation of the new line.
y - y1 = m(x - x1)
where (x1, y1) is the point (-5,2) and m is -3/5.
y - 2 = (-3/5)(x - (-5)) y - 2 = (-3/5)(x + 5) y - 2 = (-3/5)x - 3 y = (-3/5)x - 1
So the equation of the line perpendicular to 5x - 3y = 8 through the point (-5,2) is y = (-3/5)x - 1.
To find the y-intercept of this line, we set x = 0 and solve for y:
y = (-3/5)(0) - 1 y = -1
Therefore, the y-intercept of the line perpendicular to 5x - 3y = 8 through the point (-5,2) is -1.
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