Why only one of the intercepts is enough to determine a line function when the slope is constant?
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Answer:
Following equations represents a linear function:
- y = 6x
- y = 4x - √2
- x – 4y = 6
Step-by-step explanation:
We know that a linear function is of the form
where m is the rate of change or slope and b is the y-intercept.
Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.
Now, let us check whether the given functions represent the linear functions or not.
Checking y = 6x
y = 6x
comparing with the equation y = mx+b
slope = 6, and y-intercept b = 0
y = 6x is a straight line because the degree of the linear equation is always 1.
Checking x³- y = -2
x³- y = -2
As the power of x variable 3. So, its graph will no longer be a straight line,
Thus, it is not a linear function as a linear function can not have any exponent.
Hence, x³- y = -2 is not a linear function.
Checking y = 4x - √2
y = 4x - √2
comparing with the equation y = mx+b
slope = 4, and y-intercept b = -√2
Thus, y = 4x - √2 is a straight line because the degree of the linear equation is always 1. Thus, the graph of y = 4x - √2 is a straight line.
Checking x – 4y = 6
x – 4y = 6
writing the in the form y = mx+b
4y = x - 6
divide both sides by 4
4y/4 = x/4 - 6/4
y = x/4 - 3/2
comparing with the equation y = mx+b
slope = x/4, and y-intercept b = -3/2
Thus, x – 4y = 6 is a straight line because the degree of the linear equation is 1. Thus, the graph of x – 4y = 6 is a straight line.
SUMMARY:
Following equations represents a linear function:
- y = 6x
- y = 4x - √2
- x – 4y = 6