Write an equation of the line passing through (-5,-14) and (4,0.4) in form of Ax+By= C

m = -14 -.4 divided by -5 -4

-14/4/-9 14.4/9 = m

y+14 = (14.4/9)(x+5)

the equation will be in y=mx + b form and you can change it to Ax+By =C

slope = (.4 + 14)/(4+5)

= 14.4/9 = 144/90 = 8/5

so using (-5,-14)
y+14 = (8/5)(x+5)
5y + 70 = 8x + 40

8x - 5y = 30

To find the equation of a line passing through two given points in the form of Ax + By = C, we need to follow these steps:

Step 1: Calculate the slope (m) of the line using the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the given points.

Let's use the coordinates (-5, -14) and (4, 0.4):

m = (0.4 - (-14)) / (4 - (-5))
= 14.4 / 9
= 1.6

Step 2: Now that we have the slope (m), let's write the equation of the line using the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is either of the given points. Let's use the point (-5, -14):

y - (-14) = 1.6(x - (-5))
y + 14 = 1.6(x + 5)

Step 3: Simplify the equation by distributing the 1.6:

y + 14 = 1.6x + 1.6 * 5
y + 14 = 1.6x + 8

Step 4: Rearrange the equation in the standard form Ax + By = C by moving all the terms to one side:

1.6x - y = -14 + 8
1.6x - y = -6

Step 5: If needed, multiply the entire equation by a common factor to make all the coefficients integers. In this case, we can multiply by 10 to eliminate the decimals:

(10 * 1.6)x - (10 * -1)y = -6 * 10
16x + 10y = -60

Therefore, the equation of the line passing through the points (-5, -14) and (4, 0.4) in the form Ax + By = C is 16x + 10y = -60.