Question
In the xy-plane, line passes through the points (0, 1) and (1, 4). Which of the following is an equation of line ?
Hint:
Hint:
We need to find the equation of a line passing through two points on the xy-plane. We use the formula below.
The equation of a line passing through the points (a, b) and (c, d) is given by
There are other forms of this equation which are derived by manipulating the above formula.
For example,
Another way of writing the above formula is given as
The correct answer is:
According to the question, the line passes through the points (0, 1) and (1, 4).
We know,
Let (a, b) and (c, d) be two points on the xy-plane,
The equation of a line passing through the points (a, b) and (c, d) is given by
Here, we can denote
(a , b) = (0, 1)
(c , d) = (1, 4 )
By using these values of a, b, c, d in the formula above, we get
The equation of line
is given by
Further, solving the equation gives,
Expanding the equation gives,
Hence, the equation of line passing through (0, 1) and (1, 4) is given by
Thus, the correct option is C)
Note:
The points on a line in the xy-plane always satisfy the equation of the line. Here, notice that both (0, 1) and (1, 4) satisfy the equation y=3x + 1 . So, an alternate way of doing this problem is to check which equation in the options is satisfied by the given points.
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Note:
An alternate way to find the solution is to plot the given inequalities in the xy-plane. Each inequality denotes either side of the line given by putting equal sign instead of the inequality. To find which side of the line satisfies the inequality, check with point (0, 0) and shade the region satisfied by the inequality. After that, check if each of the points given in the options satisfies the region shaded in the xy-plane.
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An alternate way to find the solution is to plot the given inequalities in the xy-plane. Each inequality denotes either side of the line given by putting equal sign instead of the inequality. To find which side of the line satisfies the inequality, check with point (0, 0) and shade the region satisfied by the inequality. After that, check if each of the points given in the options satisfies the region shaded in the xy-plane.
