pre cal question

Question

Write the equation of a line through the given points in standard form Ax+By=C. (-6,1) and (-1,4)

Answer 1

The problem gives two points [ (-6,1) and (-1,4) ] and asks for the equation of the line in Standard Form [Ax+By]=C.

 

You may (1) write the equation using: (y-y₁) = m(x-x₁) = ( (y₂-y₁)/(x₂-x₁) )(x-x₁) and then (2) convert the result into Standard Form --- or you could realize that Standard From has many advantages.  So, let's just use them.

 

The two points satisfy the equation, so

           A(-6)+B(1) = A(-1)+B(4)         [plug points into line equation]

           A(-5)-B(3) = 0

    This is true for A=3 and B=-5      [note:  exchange coefficients]

 

The equation is 3x-5y=C and we could use either point to determine C.  Let's use (-1,4):

     3(-1)-5(4)=C

       -23=C

 

The answer is:   3x-5y=-23

Answer 2

Hi Mary,

Let's use Slope Intercept Form: y=mx+b

Step One: To find the slope (m) use the equation (y₂-y₁)/(x₂-x₁)=m

(-6,1) and (-1,4) is (x, y) and (x₂, y₂). Plugging in these values, we get: 

4-1/-1-(-6)=m

3/5=m

The slope is therefore 3/5

Step Two: To find the y intercept (b), we plug in a given coordinate point. Let's use (-1,4). 

(-1,4) is (x,y)

y=mx+b

4=3/5(-1)+b

4=-3/5+b

4+3/5=b

b=4.6

Our equation in slope-intercept form y=mx=b is therefore y=3x/5+4.43

Step Three: Change this into Standard form Ax+By=C

y=3x/5+4.43

5y=3x+23

5y-3x=23

3x-5y=-23

Sincerely, 

Starlyte H.

Answer 3

Mary, remember the algebra from prior courses.

 

First, calculate slope.

 

Then use point-slope form of the equation of a line, using either one of the given points.

 

finally, clear fractions (if needed) & put both x & y terms on left side of equation, and the constant only on the right side.