Answer:
The equation is 2y + 5x = 2
Step-by-step explanation:
The two points given are (x1 , y1) = (4,-9) and (x2 , y2) = (2,-4)
Step 1: find out the slope of the equation
Slope m of any equation = [tex]\frac{y_{2} - y{1}}{x_{2} - x_{1}}} = \frac{-4-(-9)}{2 -4} = \frac{-4 + 9}{-2} = -\frac{5}{2}[/tex]
Hence, m = (-5/2)
Step 2: Substitue m in the equation y = mx + b
⇒[tex]y = \frac{-5}{2} x+ b \\ or, 2y + 5x = b[/tex]
Step 3: put any of the two points in above equation and find y-intercept b
⇒Using (2,-4), we get 2y + 5x = 2(-4) + 5 (2) = -8 + 10 = 2
⇒ b = 2
Step 4: Substitute the value of b in the above equation
we get, 2y + 5x = b = 2
Hence, the equation is 2y + 5x = 2
