A straight-line graph
1 answer:
Given:
A straight-line graph has gradient 4 and crosses the y axis at (0, −3).
To find:
The equation of the given graph.
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope of the line and b is the y-intercept.
A straight-line graph has gradient 4. It means the slope of the line is 4.
Line crosses the y axis at (0, −3). So, y-intercept is -3.
Putting m=4 and b=-3 in (i), we get
Therefore, the equation of the given line graph is .
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Rearrange 
to give
Let
be a variable 'p' and so we can write 
as 
Rewrite the equation in terms of 'p'
where
using the quadratic formula
and subsitute the value of 
There are two value of p; 125 and -27
Now we find the value of x
Earlier we substitute
for 
and for 
When
, ![x= \sqrt[3]{125}=5](https://tex.z-dn.net/?f=x%3D%20%5Csqrt%5B3%5D%7B125%7D%3D5%20)
When![p = -27, x= \sqrt[3]{-27}=-3](https://tex.z-dn.net/?f=p%20%3D%20-27%2C%20x%3D%20%5Csqrt%5B3%5D%7B-27%7D%3D-3%20)
So the final answer is the two values of x;
x = 5 OR x = -3
Let
Rewrite the equation in terms of 'p'
where
using the quadratic formula
There are two value of p; 125 and -27
Now we find the value of x
Earlier we substitute
When
When
So the final answer is the two values of x;
x = 5 OR x = -3