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Question 95944: Give the slope-intercept form of the equation for the line on which these two points lie: (4, -2) and (3, 8)
Found 2 solutions by checkley71, bucky:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! SLOPE=(Y2-Y1)/(X2-X1)=(8+2)/(3-4)=10/-1=-10 FOR THE SLOPE
NOEW SUBSTITUTE THE X&Y VALES FROM 1 POINT & SOLVE FOR THE Y INTERCEPT (b) IN THE LINE FORMULA [Y=mX+b]
-2=-10*4+b
-2=-40+b
b=40-2
b=38 THE Y INTERCEPT.
THUS THE LINE EQUATION IS:
Y=-10X+38
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 40, y = -10x +38).
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! The slope-intercept form of an equation is:
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y = mx + b
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in which m is the slope and b is the value of y at the point on the y-axis where the graph
intersects the y-axis.
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We know that the two points (4, -2) and (3, 8) will satisfy the equation. So we can establish
two equations, one for each point.
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For the first point we substitute 4 for x and -2 for y in the slope-intercept form. This
results in:
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-2 = m4 + b
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Rearranging this into a more standard form results in:
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4m + b = -2 <==== remember this as "equation 1"
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Now let's do the same thing for the second point. In the second point x = 3 and y = 8.
Substituting these values into the slope-intercept form of y = mx + b results in:
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8 = m3 + b
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Rearrange this into a more standard form results in:
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3m + b = 8 <==== remember this as "equation 2"
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So now we have two independent equations (equation 1 and equation 2) as follows:
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4m + b = -2
3m + b = 8
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Suppose we subtract these two equations vertically. 4m minus 3m results in just m. Then
b minus b is zero. Finally -2 minus 8 is -10. Therefore, this subtraction is:
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m = -10
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Now we can substitute this value for m into either of the two equations and solve the
resulting equation for b. For example, let's take the equation 4m + b = -2. When we substitute
-10 for m the equation becomes:
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4(-10) + b = -2
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Doing the multiplication on the left side results in:
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-40 + b = -2
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Get rid of the -40 on the left side by adding +40 to both sides of the equation. When you
add 40 to both sides the result is:
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b = -2 + 40 = +38
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So now we know that m = -10 and b = 38. Substitute these two values into the slope-intercept
form y = mx + b and the equation becomes:
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y = -10x + 38
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This is the equation you are looking for. You can check this equation by substituting
the two points, one at a time, into this resulting equation and we should see that this
equation balances for each of the points.
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Take the point (4, -2) which has x = 4 and y = -2. Substitute these values into the equation
y = -10x + 38. When you substitute 4 for x and -2 for y this equation becomes:
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-2 = -10(4) + 38
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Multiply on the right side to get:
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-2 = -40 + 38
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Combining the terms on the right side results in:
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-2 = -2
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So the point (4, -2) satisfies our answer.
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Now let's try our answer y = -10x + 38 using the point (3, 8). Substitute 3 for x and 8 for
y and our answer becomes:
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8 = -10(3) + 38
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After doing the multiplication on the right side this equation becomes:
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8 = -30 + 38
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Combining the two terms on the right side results in:
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8 = 8
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So the point (3, 8) also satisfies our answer.
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Since both points satisfy our answer, we can say that it is a correct answer for the conditions
set up in the problem. The answer to this problem is:
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y = -10x + 38
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Hope this helps you to understand the problem and one way of solving it.
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