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How do you graph 3x5y=15 using intercepts?

Answer
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Hint: As we know that there are two kinds of intercepts which are x -intercept and y -intercept. So, x -intercept is the point where the line intersects the x -axis and y -intercept is the point where the line intersects the y -axis. So, to calculate the intercepts, we will put x and y 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:
 3x5y=15
As we are asked to draw the graph of 3x5y=15 using intercepts, we first need to calculate both of the intersects namely, x -intercept and y -intercept.
Now, as we know that x -intercept is the point where the line crosses the x -axis and we also know that on x -axis, y=0 . Therefore, to find the x -intercept, we will put y as 0 in the equation of line given to us. Therefore,
 3x5(0)=153x=15x=153x=5
Therefore, the x -intercept of the equation 3x5y=15 is 5 .
(ii)
Similar to x -intercept, y -intercept is the point where the line crosses the y -axis and we also know that on y -axis, x =0. Therefore, to find y -intercept, we will put x as 0 in the equation of the line given to us. Therefore,
 3(0)5y=155y=15y=155y=3
Therefore, the y -intercept of the equation 3x5y=15 is 3 .
(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 x -axis when x=5 as the x -intercept of the given line is 5 and we also know that on the x -axis, y=0 . So, we have a point (5,0) which lies on the line 3x5y=15 .
Similarly, the line crosses the y -axis when y=3 as the y -intercept of the given line is 3 and we also know that on the y -axis, x=0 . So, we have another point which lies on the line 3x5y=15 as (0,3) .
Marking these two points on a graph and then joining the points through a line will give us the graphical representation of the line 3x5y=15 .
seo images

Hence, this is the line 3x5y=15 drawn on a graph.

Note: In an equation of the form y=mx+c , m represents the slope of the line and c represents the vertical intercept or y -intercept of the line as it is the value of y when x=0 . 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., xa+yb=1 , where a is the x -intercept and b is the y -intercept.
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