document.write( "Question 24641: I need help on POINT SLOPE FORM. I am studying for my midterms. \"m=%285%29-%284%29%28-1%29-%28-3%29=1%2F2\" Then I have to put it into point slope form. I need help with the steps and remembering how to do them. I hope you can help me! Thank you! \n" ); document.write( "
Algebra.Com's Answer #13158 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
There are lots of ways to remember the meaning of slope.
\n" ); document.write( "Say you're climbing up a ramp that goes to the top of a vertical wall.
\n" ); document.write( "You get to the top of the wall, and you say \"Boy are my legs tired.
\n" ); document.write( "My legs are twice as tired as yesterday when I climbed that other ramp,
\n" ); document.write( "but I know the wall was the same height as this one.\"
\n" ); document.write( "The slope of this ramp must be greater.
\n" ); document.write( "What do I mean by slope? Steepness. If it's really steep, I'm going to
\n" ); document.write( "struggle and my legs will get very tired.
\n" ); document.write( "OK, mathematically what do I mean by steep?
\n" ); document.write( "It's how much the ramp goes up divided by the distance to the wall that
\n" ); document.write( "I paced off on the ground. That's steepness.
\n" ); document.write( "If you draw it on a graph with x and y coordinates, it's the same thing.
\n" ); document.write( "The height of the ramp is:
\n" ); document.write( "y at the top of the ramp MINUS y at the bottom of the ramp
\n" ); document.write( "The distance to the wall on the ground is:
\n" ); document.write( "x at the wall MINUS x where the ramp began
\n" ); document.write( "The slope formula is:
\n" ); document.write( "\"%28y%28top%29+-+y%28bottom%29%29+%2F+%28x+%28at_wall%29+-+x%28start_of_ramp%29%29\"
\n" ); document.write( "or, the same thing:
\n" ); document.write( "\"%28y1+-+y0%29+%2F+%28x1+-+x0%29\"
\n" ); document.write( "Look at the equation you were given. What must the numbers represent?
\n" ); document.write( "y1 = 5
\n" ); document.write( "y0 = 4
\n" ); document.write( "x1 = -1
\n" ); document.write( "x0 = -3
\n" ); document.write( "m = 1/2
\n" ); document.write( "Now you can write the formula this way:
\n" ); document.write( "\"%28y+-+y0%29+%2F+%28x+-+x0%29\" That's where (x,y) is any old point on the line
\n" ); document.write( "(ramp), but everything still holds true.
\n" ); document.write( "\"1%2F2+=+%28y+-+4%29+%2F+%28x+-+%28-3%29%29\"
\n" ); document.write( "reorder this so it looks like y = mx + b
\n" ); document.write( "\"%28y+-+4%29+=+%281%2F2%29+%2A+%28+x+-+%28-3%29%29\"
\n" ); document.write( "\"y+=+%281%2F2%29+%2A+x+%2B+3%2F2+%2B+4\"
\n" ); document.write( "\"y+=+%281%2F2%29+%2A+x+%2B+11%2F2\"
\n" ); document.write( "lets check this. The slope is 1/2 That's OK
\n" ); document.write( "What about the 11/2?
\n" ); document.write( "That's what y is if you make x = 0
\n" ); document.write( "It's the point (0, 11/2). If I plug it into the slope formula, I should get 1/2.
\n" ); document.write( "(0, 11/2) is my new (x1, y1)
\n" ); document.write( "\"%2811%2F2+-+4%29+%2F+%280+-+%28-3%29%29\"
\n" ); document.write( "\"%283%2F2%29+%2F+3\"
\n" ); document.write( "this equals 1/2, so all is well
\n" ); document.write( "I hope you're OK with all of this \n" ); document.write( "
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