The line passing through the origin and parallel to the line passing through points (8,5) and (-9,3)

Question

Find the equation of the line that satisfies the given condition

 

 

Answer 1

Start by drawing yourself a graph and plotting the two points. Then draw the line that connects them. This will help you visualize the problem. 

 

There are two steps to this problem first we need to figure out the slope of the line that passes tbrought the points (8, 5) and (-9, 3). To find the slope we use the formula for rise/run. Rise refers to the y axis because it goes up. Run refers to the x axis because it goes forward. 

 

Rise/Run = (y1-y2)/(x1-x2)

 

The 1 and 2 refer to which point. It does not matter which point you choose to make 1 or 2. 

 

So (8,5) = (x1, y1)

(-9, 3) = (x2, y2)

 

Now put the numbers in the formula. 

m= (y1-y2)/(x1-x2)

 

m = (5-3)/(8-(-9))

m = 2/ 17

 

This gives us the slope. So now we have part of the equation. The standard form of a line is y=mx +b.

 

since the line we are looking for is parallel to the above that tells us that the slopes are the same. 

 

The line whose equation we want goes through the origin which gives a point (0,0) and we know the slope m= 2/17. 

 

Now we need to find the y-intercept (b) of the equation we are trying to find. 

 

To to do this we can insert the point into the equation and solve for b.

 

y=mx+b

0 = (2/17)(0) + b

0 = b

 

now we have all the parts needed for the equation of the line

 

y =(2/17)x + 0

y = (2/17)x