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

Algebra ->  Systems-of-equations -> 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       Log On


   

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(20850) About Me  (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 a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%286-10%29%2F%281-3%29+=+2.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 2%2A3+%2Bb+=+4. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=10-2%2A3+=+4.

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 x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=1.5, and system%28+x%5B1%5D+=+2%2C+y%5B1%5D+=+5+%29+, we have the equation of the line:

y=1.5%2Ax+%2B+2

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? 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 (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

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 a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%285-7%29%2F%282-1%29+=+-2.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -2%2A1+%2Bb+=+9. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=7--2%2A1+=+9.

y=(-2)x + (9)

Your graph: