Question
Which of the following is an equation of line l in the xy-plane above?
- x = 1
- y = 1
- y = x
- y = x +1
Hint:
To find the equation of given line we should first know the standard equation of Straight line i.e.
y= mx + c
where m = slope of the line,
c = y-intercept of the line
(x, y) represent every point on the line
x and y have to be kept as the variables while applying the above formula.
If (x1,y1) and (x2,y2) are the points on a line , then the slope of line ,
The correct answer is: y = x +1
Lets take two points on the line A(0,1) and B(3,4)
- Slope of the given line,
=
m = 1
- Lets calculate the y- intercept – Y intercept is the value of y when x= 0 ,
Therefore, y intercept, c= 1
- Put the values of slope m and y-intercept c in the equation y= mx+c
- y = (1)x + 1
y= x + 1
- Therefore, the correct answer is option (D) y= x + 1
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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.
