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

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To determine the equation of a line through the point (6, -4) and perpendicular to the line represented by -7x + 5y = -62, first convert the given line into slope-intercept form (y = mx + b). The slope of the original line is 7/5, so the slope of the perpendicular line will be the negative reciprocal, which is -5/7. Using the point-slope formula with the point (6, -4) and the slope -5/7, the equation of the desired line can be derived. The final equation in slope-intercept form is y = -5/7x + 18/7. This approach effectively utilizes the properties of perpendicular lines to find the required equation.
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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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