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MArishka [77]
2 years ago
6

Caleb drives for 3 hours at 15 mph. how far does he travel

Mathematics
1 answer:
atroni [7]2 years ago
7 0
He travels approximately 45 miles
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This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where 
m=slope of line
(x0,y0) is a point through which the line passes.

We know that the line passes through A(3,-6), B(1,2)

All options have a slope of -4, so that should not be a problem.  In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.

So we can check which line passes through which point:

a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3)  means that line passes through A(3,-6) => ok

b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
   ****** this equation is not the line passing through A & B *****

c. y=-4x+6  subtract 2 from both sides (to make the y-coordinate 2)
   y-2 = -4x+4, rearrange
   y-2 = -4(x-1)  
   which means that it passes through B(1,2), so ok

d. y-2=-4(x-1)
   this is the same as the previous equation, so it passes through B(1,2), 
   this equation is ok.

Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
   
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Write the equation of the line that passes through the points (-9, -8) and (–6,6).
sveta [45]

Answer:

Slope - intercept form    y = \frac{14}{3} x  + 34

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given points are ( -9 ,-8 ) and (-6,6)

slope of given two points

    m = \frac{y_{2} -y_{1} }{x_{2}-x_{1}  } = \frac{6-(-8)}{-6-(-9)} = \frac{14}{3}

The equation of the straight line passing through the points and having slope

          y - y_{1} = m ( x - x_{1} )

        y - (-8) = \frac{14}{3}  ( x - (-9) )

          3 y + 2 4 = 14 x + 126

           3 y = 14 x + 126 - 24

          3 y = 14 x + 102

            y = \frac{14}{3} + \frac{102}{3}

           y = \frac{14}{3} x  + 34

Slope - intercept form  y= mx +C

Slope - intercept form    y = \frac{14}{3} x  + 34

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