The line 2y +px +4= 0 passes through the point (-4,4) where p is a constant find the gradient of the line
To find the gradient of the line, we need to first rewrite the equation of the line in the slope-intercept form (y = mx + b), where m represents the gradient.
Given equation: 2y + px + 4 = 0
Substituting (-4,4) into the equation:
2(4) + p(-4) + 4 = 0
8 - 4p + 4 = 0
12 - 4p = 0
4p = 12
p = 12/4
p = 3
The value of p is 3.
Substituting p = 3 into the equation 2y + px + 4 = 0:
2y + 3x + 4 = 0
Now the equation is in the form y = mx + b, where m = 3.
Therefore, the gradient of the line is 3.