Question

standard form for (-2,4),(2,-1)

Answer 1

To write the standard form of a linear equation, we need to find the values of A, B, and C in the equation Ax + By = C.

Given the two points (-2, 4) and (2, -1), we can find the slope of the line using the formula:

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

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

Now, we can use the slope-intercept form of a line (y = mx + b) and substitute one of the points into it to find the y-intercept (b):

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

The slope-intercept form is y = (-5/4)x + 3/2.

To convert this to standard form, we need to get rid of the fraction. Multiply the equation by 4 to clear the fraction:

4y = (-5/4)(4x) + (3/2)(4)
4y = -5x + 6

Next, we bring all the terms to the left side of the equation and combine like terms:

5x + 4y = 6

Therefore, the standard form of the equation is 5x + 4y = 6.