
How do you graph using intercepts?
Answer
466.2k+ views
Hint: As we know that there are two kinds of intercepts which are -intercept and -intercept. So, -intercept is the point where the line intersects the -axis and -intercept is the point where the line intersects the -axis. So, to calculate the intercepts, we will put and as zero one by one and then once we get both the intercepts, we will use the coordinates of the intercepts and draw the line on a graph.
Complete step-by-step answer:
(i)
We are given the line equation:
As we are asked to draw the graph of using intercepts, we first need to calculate both of the intersects namely, -intercept and -intercept.
Now, as we know that -intercept is the point where the line crosses the -axis and we also know that on -axis, . Therefore, to find the -intercept, we will put as in the equation of line given to us. Therefore,
Therefore, the -intercept of the equation is .
(ii)
Similar to -intercept, -intercept is the point where the line crosses the -axis and we also know that on -axis, =0. Therefore, to find -intercept, we will put as in the equation of the line given to us. Therefore,
Therefore, the -intercept of the equation is .
(iii)
Now, to draw a graph we need two points which lie on the line. As we have calculated both the intercepts, we can say that the line crosses the -axis when as the -intercept of the given line is and we also know that on the -axis, . So, we have a point which lies on the line .
Similarly, the line crosses the -axis when as the -intercept of the given line is and we also know that on the -axis, . So, we have another point which lies on the line as .
Marking these two points on a graph and then joining the points through a line will give us the graphical representation of the line .
Hence, this is the line drawn on a graph.
Note: In an equation of the form , represents the slope of the line and represents the vertical intercept or -intercept of the line as it is the value of when . Also, there is an alternative method to find the intercepts of a line equation. Convert the given line equation into intercept form of a line i.e., , where is the -intercept and is the -intercept.
Complete step-by-step answer:
(i)
We are given the line equation:
As we are asked to draw the graph of
Now, as we know that
Therefore, the
(ii)
Similar to
Therefore, the
(iii)
Now, to draw a graph we need two points which lie on the line. As we have calculated both the intercepts, we can say that the line crosses the
Similarly, the line crosses the
Marking these two points on a graph and then joining the points through a line will give us the graphical representation of the line

Hence, this is the line
Note: In an equation of the form
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