From the differential equation of the family of straight lines having y-intercept 3
To find the differential equation of the family of straight lines with a y-intercept of 3, we need to use the slope-intercept form of a straight line equation, which is:
y = mx + b
where:
- y is the dependent variable (usually representing the vertical axis),
- x is the independent variable (usually representing the horizontal axis),
- m is the slope of the line,
- b is the y-intercept.
In this case, the y-intercept is given as 3. So we have:
y = mx + 3.
To determine the differential equation, we need to differentiate both sides of this equation with respect to x. Remember that the derivative of a constant (in this case, 3) is zero. The derivative of y with respect to x will give us the slope of the line. So:
dy/dx = m.
Therefore, the differential equation for the family of straight lines with a y-intercept of 3 is:
dy/dx = m.
Here, m represents the slope of any particular line from the given family.
what equation??
clearly the family is
y = mx+3