Question

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

Answer 1

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.