The equation of a line is y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ----> (0, y) or the point where the line goes through the y-axis]
To find the slope, you use the slope formula (m):
and plug in 2 points
I will use the points (0, 0) and (1, 8)
(0, 0) ----> (x₁, y₁)
(1, 8) ----> (x₂, y₂)
m = 8
Since you know m, plug it into the equation.
y = 8x + b
The graph shows that the y-intercept is 0, so plug it into the equation
y = 8x
Given:
The equation of a function is
To find:
The graph of the given function.
Solution:
The vertex form of a parabola is
...(i)
Where, (h,k) is vertex of the parabola.
We have,
...(ii)
From (i) and (ii), we get
The vertex of the parabola is (4,1).
Now, the table of values is
x y
2 5
3 2
4 1
5 2
6 5
Plot these points on a coordinate plane and connect them by a free hand curve.
The graph of given function is shown below.
