Soldier Brown is on a field expedition. She needs to determine her location. Her partner radios her the coordinates of Mount Blue, but she cannot see it. She can see Mountain Azure and knows its coordinates are (3,5) and the slope of the line from Mountain Azure to her location is -2. She can also see a water tower and knows from his map that the coordinates of the water tower are (9,3) and the slope of the line from the water tower to her location is 1/2. Her location is (x,y) where the two lines intersect. Write an equation of the line that passes through Soldier Brown’s location
and Mountain Azure’s location.
Write an equation (in standard form) of the line that passes through Mountain Azure's location and Soldier Brown's location.
Write an equation of the line that passes through Soldier Brown’s location
and the water tower's location.
Use the equations from Exercises 1 and 2 to form a system of equations.
and Mountain Azure’s location.
Write an equation (in standard form) of the line that passes through Mountain Azure's location and Soldier Brown's location.
Write an equation of the line that passes through Soldier Brown’s location
and the water tower's location.
Use the equations from Exercises 1 and 2 to form a system of equations.
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Equation of a straight line is given by y=mx+c. m, the gradient, can be attained by dividing the change in y coordinates between two points of the line, by the change in x coordinates between two points of the line. Positive values of m are taken to mean that the slope is rising, negative values mean the slope is falling.
In this example, Soldier Brown is standing below Mount Azure (as one might expect given that it's a mountain), and above the water tower.
We don't, at this point need to find x and y to work out the equation of the line required. Since we know that m is gradient and it tells us that gradient is -2, we just dump it into the equation to get y=-2x+c, for some c. We find c using the coordinates of Mount Azure (stick (3,5) into the equation and go for it).
Once you've done all the bits that're of that format, you then form equations relating the gradients to (x,y). In the case of Mount Azure, (y-5)/(x-3)=-2. (Change in y over change in x). The instructions don't tell you to find x and y, which I consider odd, but you could if you wanted to, 'cause you'll end up with simultaneous equations in x and y.
Hope this helps (didn't want to do it all for you).
In this example, Soldier Brown is standing below Mount Azure (as one might expect given that it's a mountain), and above the water tower.
We don't, at this point need to find x and y to work out the equation of the line required. Since we know that m is gradient and it tells us that gradient is -2, we just dump it into the equation to get y=-2x+c, for some c. We find c using the coordinates of Mount Azure (stick (3,5) into the equation and go for it).
Once you've done all the bits that're of that format, you then form equations relating the gradients to (x,y). In the case of Mount Azure, (y-5)/(x-3)=-2. (Change in y over change in x). The instructions don't tell you to find x and y, which I consider odd, but you could if you wanted to, 'cause you'll end up with simultaneous equations in x and y.
Hope this helps (didn't want to do it all for you).
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Y =mx + b
M = slope
B = y-intercept
Make equations for both coordinates and set them equal to eachother and solve for x
M = slope
B = y-intercept
Make equations for both coordinates and set them equal to eachother and solve for x