Question

How do you find the x and y-intercept of \[5x + 3y = 30\]?

Answer 1

Hint: If a point crosses the x-axis, then it is called x-intercept. If a point crosses the y-axis, then it is called y-intercept. To find the x and y-intercept of the given equation, for y-intercept we need to substitute \[x\]= 0 in the given equation and solve for y, and for x-intercept substitute y = 0 in the given equation and solve for x.

Complete step-by-step solution:
The given equation is
\[5x + 3y = 30\]
To find the x-intercept, substitute y = 0 in the given equation and solve for x i.e.,
\[5x + 3\left( 0 \right) = 30\]
After simplifying we get
\[5x = 30\]
Divide both sides by 5 to get the value of x as
\[\dfrac{{5x}}{5} = \dfrac{{30}}{5}\]
\[x = \dfrac{{30}}{5}\]
Therefore, the value of x is
\[x = 6\]
Hence, the x-intercept of \[5x + 3y = 30\] is \[\left( {6,0} \right)\].
To find the y-intercept, substitute \[x\]= 0 in the given equation and solve for y i.e.,
\[5x + 3y = 30\]
\[5\left( 0 \right) + 3y = 30\]
After simplifying we get
\[3y = 30\]
Divide both sides by 3 to get the value of y as
\[\dfrac{{3y}}{3} = \dfrac{{30}}{3}\]
\[y = \dfrac{{30}}{3}\]
Therefore, the value of y is
\[y = 10\]
Hence, the y-intercept of \[5x + 3y = 30\] is \[\left( {0,10} \right)\].
Therefore, the x and y-intercept of \[5x + 3y = 30\] is
\[\left( {6,0} \right)\]and \[\left( {0,10} \right)\].

Additional information:
The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called x-intercept. If a point crosses the y-axis, then it is called y-intercept. If the axis is not specified, usually the y-axis is considered. It is y-coordinate of a point where a straight line or a curve intersects the y-axis.

Note: As per the given equation consists of x and y terms based on the intercept asked, we need to solve for it. For ex if y-intercept is asked substitute x=0 and solve for y and if x-intercept is asked substitute y=0 and solve for x and the y-intercept of an equation is a point where the graph of the equation intersects the y-axis.