SOLUTION: Find the equations of the following lines. A. Passing through (3,10) and (I,6). B. With slope 1.5 and passing through (2,5). C. Passing through (1,7) and falling 2 units in for

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Question 1165921: Find the equations of the following lines.
A. Passing through (3,10) and (I,6).
B. With slope 1.5 and passing through (2,5).
C. Passing through (1,7) and falling 2 units in for each increase of 1 in x.
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

a.
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (3, 10) and (x2, y2) = (1, 6).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(2)x + (4)

Your graph:



b.
Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (2, 5)

  • it has a slope of 1.5



First, let's draw a diagram of the coordinate system with point (2, 5) plotted with a little blue dot:



Write this down: the formula for the equation, given point and intercept a, is

(see a paragraph below explaining why this formula is correct)

Given that a=1.5, and , we have the equation of the line:



Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: .

Here's the graph:




C. Passing through (1,7) and falling 2 units in for each increase of 1 in x.
if so, next point will be (1+1,7-2)=(2,5)
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 7) and (x2, y2) = (2, 5).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(-2)x + (9)

Your graph:
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