Determine equation of line described. put in slope intercept form if possible

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SUMMARY

The discussion focuses on determining the equation of a line that passes through the point (6, -4) and is perpendicular to the line represented by the equation -7x + 5y = -62. To find the required line's equation, the slope of the given line must first be converted to slope-intercept form (y = mx + b). The slope of the original line is calculated as 7/5, and the slope of the perpendicular line is the negative reciprocal, which is -5/7. Using the point-slope formula, the final equation of the line can be derived.

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okay so as usual I am stumped ( I am not sure if I dislike math, or simply those who proclaim to be teachers of it. Spouting off steps is not the same thing as teaching ) Anyway, I have a problem that requires me to determine the equation of the line described:

Through (6,-4), perpendicular to -7x +5y=-62

Any help is greatly appreciated.
 
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Okay, we are given one point on the line, and we are told this line is perpendicular to the line:

$$-7x +5y=-62$$

We need to find the slope of this line, so that we may use the negative reciprocal of this slope as the slope of the line we are asked to find. This way we will have a point and the slope, and then we can apply the point-slope formula to obtain the equation of the line in question.

So, can you arrange the given line in slope-intercept form:

$$y=mx+b$$ ?
 

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