+0  
 
0
7
1
avatar+16 

Write the equation of the line below in the form A(x) + B(x) = C, where A, B, and C are integers with greatest common divisor 1, and A is positive.

The line consists of two known points:  (-4, 2) and (1, -1)

 Apr 8, 2024
edited by Seraphspace  Apr 8, 2024
 #1
avatar+1211 
0

Finding the Slope (m):

 

The slope (m) of the line passing through points (-4, 2) and (1, -1) can be found using the following formula:

 

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

 

Here, (x1, y1) = (-4, 2) and (x2, y2) = (1, -1)

 

m = (-1 - 2) / (1 - (-4)) = -3 / 5

 

Finding the y-intercept (b):

 

We can use the point-slope form of the equation to find the y-intercept (b). Here, we can use either of the given points. Let's use (-4, 2).

 

y = mx + b

 

2 = (-3/5) * (-4) + b

 

2 = 12/5 + b

 

b = 2 - 12/5 = -2/5

 

Writing the Equation in Ax + By = C form:

 

Now, we can express the equation in the desired form:

 

A(x) + B(y) = C

 

Substitute the slope (m) and y-intercept (b):

 

A(x) + (-3/5)(y) = -2/5

 

Finding A, B, and C with GCD = 1 and A positive:

 

To ensure the greatest common divisor (GCD) of A, B, and C is 1 and A is positive, we can multiply the entire equation by the least common multiple (LCM) of the denominators of m and b (which is 5 in this case).

 

5A(x) - 3y = -2

 

Since A is positive, we can simply set A = 5:

 

5(x) - 3y = -2

 

Therefore, the equation of the line in the desired form is:

 

5x - 3y = -2

 Apr 14, 2024

0 Online Users