document.write( "Question 565299: Hi, can i please get some steps on how to do this question: Find the value of \"k\" if the line y=-5/2x +2 is perpendicular to this line 4x+ky=7 \n" ); document.write( "
Algebra.Com's Answer #365770 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
your first equation is already in slope intercept form.
\n" ); document.write( "slope intercept form is y = mx + b
\n" ); document.write( "m is the slope and b is the y intercept.
\n" ); document.write( "the y intercept is the value of y when x = 0.
\n" ); document.write( "your second equation is in standard form.
\n" ); document.write( "standard form is ax + by = c
\n" ); document.write( "you need to convert the equation from standard form to slope intercept form before you do anything else.
\n" ); document.write( "start with 4x + ky = 7
\n" ); document.write( "subtract 4x from both sides of this equation to get:
\n" ); document.write( "ky = -4x + 7
\n" ); document.write( "divide both sides of the equation by k to get:
\n" ); document.write( "y = (-4/k)x + (7/k)
\n" ); document.write( "your 2 equations are now:
\n" ); document.write( "y = (-5/2)x + 2
\n" ); document.write( "y = (-4/k)x + (7/k)
\n" ); document.write( "if the lines are perpendicular, then their sloped are negative reciprocals of each other,.
\n" ); document.write( "the slope of the first equation is equal to (-5/2).
\n" ); document.write( "the negative reciprocal of (-5/2) is equal to (2/5)
\n" ); document.write( "since the line determined by your second equation is perpendicular to the line determined by your first equation, this means that:
\n" ); document.write( "(-4/k) = (2/5)
\n" ); document.write( "you can solve for k by doing the following:
\n" ); document.write( "equation is:
\n" ); document.write( "-4/k = 2/5
\n" ); document.write( "multiply both sides of this equation by k to get:
\n" ); document.write( "-4 = 2k/5
\n" ); document.write( "multiply both sides of this equation by 5/2 to get:
\n" ); document.write( "-4*5/2 = k
\n" ); document.write( "this makes k equal to -10
\n" ); document.write( "the slope of your second equation becomes:
\n" ); document.write( "slope = -4/k = -4/-10 = 4/10 = 2/5
\n" ); document.write( "2/5 is the negative reciprocal of -5/2 so we got the slope right.
\n" ); document.write( "your second equation becomes:
\n" ); document.write( "y = (2/5)x + 7/k
\n" ); document.write( "since k is equal to -10, your equation becomes:
\n" ); document.write( "y = (2/5)x - (7/10)
\n" ); document.write( "you can now graph these equations to see how they look.
\n" ); document.write( "the equations are:
\n" ); document.write( "y = -(5/2)x + 2
\n" ); document.write( "y = (2/5)x - (7/10)
\n" ); document.write( "\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-%285%2F2%29x%2B2%2C%282%2F5%29x-%287%2F10%29%29\"\r
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