Question

‌‌How‌ ‌do‌ ‌you‌ ‌find‌ ‌the‌ ‌x ‌and‌ ‌y intercept‌ ‌of‌ ‌5x+y=2 ‌?

Answer 1

In order to find the solution for this linear equation, we will first substitute $0$ for $y$ and solve for $x$ to find the $x$ -intercept. Then, we will first substitute $0$ for $x$ and solve for $y$ to find the $y$ -intercept. That is, we will use a substitution method.

Complete step by step solution:
As we know our given problem is a linear equation of line.
So when this line crosses the $y$ -axis, the $x$ -coordinate will be zero.
Also, when this line crosses the $x$ -axis, the $y$ -coordinate will be zero.
We have our equation of line as:
$5x+y=2$
when the line crosses the $y$ -axis, the $x$ -coordinate will be zero
Therefore, now we will substitute $x=0$into the equation.
This will allow us to obtain the corresponding $y$ -coordinate ($y$ -intercept).
Therefore, we get:
$5\left( 0 \right)+y=2$
$0+y=2$
$y=2$
Therefore, $y=2$ is the required $y$ -intercept.
Similarly, when this line crosses the $x$ -axis, the $y$ -coordinate will be zero.
Therefore, now we will substitute $y=0$ into the equation.
This will allow us to obtain the corresponding $x$ -coordinate ($x$ -intercept).
Therefore, we get:
$5x+0=2$
$5x=2$
$x=\dfrac{2}{5}$
Therefore, $x=\dfrac{2}{5}$ is the required $x$ -intercept.
Therefore, $x$ -intercept $=\dfrac{2}{5}$ and $y$ -intercept $=2$.

Note: The $x$ -intercept is the point where a line crosses the $x$-axis, and the $y$ -intercept is the point where a line crosses the $y$-axis. The above linear equation can be written in the form $y=mx+c$. The slope-intercept is the most “popular” form of a straight line. This is useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and $y$ -intercept can easily be identified or read off from this form.