Given:
The equation is:
To find:
The slope intercept form of the given equation.
Solution:
Slope intercept form of a line is:
Where, m is slope and b is y-intercept.
We have,
It is not in the slope intercept form.
We need to isolate variable y to get the slope intercept form.
The given equation can be rewritten as:
Therefore, the slope intercept form of the given equation is .
Answer:
y = x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (4, 7)
m = =
= 1, hence
y = x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using (1, 4), then
4 = 1 + c ⇒ c = 4 - 1 = 3
y = x + 3 ← equation in slope- intercept form
The Lagrangian is
with critical points where the partial derivatives vanish.
Substitute into the last equation and solve for
:
Then we get two critical points,
We get an absolute maximum of at the second point, and an absolute minimum of
at the first point.