Question

Determine the standard form of the equation of the line that passes through (-8, -6) and (-4, 9)

Answer 1

The standard form of the equation is 3.75x - y + 30 = 0.

Step-by-step explanation:

To find the standard form of the equation of a line, we need to determine the values of A, B, and C where Ax + By = C.

Given two points (-8, -6) and (-4, 9), we can find the slope using the formula:

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

Plugging in the coordinates, we get m = (9 - (-6)) / (-4 - (-8)) = 15 / 4 = 3.75.

Now, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (-8, -6), we have y - (-6) = 3.75(x - (-8)). Simplifying, we get y + 6 = 3.75(x + 8).

Next, we can expand and rearrange the equation to get it in standard form:

3.75x - y + 30 = 0.

Answer 2

15/4 x-y=-24

Step-by-step explanation:

the standard form is ax+by=c

two points (x1,x2) , (y2,y1)

x1=-8 x2=-6

y1=-4 y2=9

find slope m: y2-y1/x2-x1

m=9-(-6)/-4-(-8)

m=15/4

find b: take any point(-8,-6)

y=mx+b

-6=15/4 (-8)+b

-6=-30+b

b=-6+30

b=24

y=15/4 x+24

standard form: y-15/4x=24

OR : 15/4 x-y=-24