Question

How do you graph using the intercepts for $-x-7y=14$

Answer 1

Hint: First we find the axis intercept values in the given equation. Also, when it is either $x$ or $y$ values are $0$. Then we have to plot the intercepts for the given equation in the graph. Finally we get the required solution.

Complete step-by-step solution:
It is given that the question we have to find the $x-$ intercept and $y-$ intercept for the straight line: $-x-7y=14$
Before we start solving this question, let us see what the $x-$ intercept and the $y-$ intercept which is also known as horizontal intercept and vertical intercept by putting $x=0\text{, y = 0 }$ for each one respectively.
Our equation is linear function; the two intercepts can be calculated as follows:
Substituting $x=0$ in the given equation ie., $-x-7y=14$
$\Rightarrow -(0)-7y=14$
On rewriting we get,
$\Rightarrow -7y=14$
On dividing $$-7$$ on both sides we get,
$\Rightarrow y={\displaystyle \frac{14}{-7}}$
Let us divide the term and we get,
$\Rightarrow y=-2$
Hence we get the $x-$ intercept value.
$\therefore$$x-$ Intercept is $y=-2$
Also, we need to find $y-$ intercept.
Now we are substitute, $y=0$ in the given equation,
$\Rightarrow -x-7y=14$
On putting the value of zero in place of $y.$
 $\Rightarrow -x-7(0)=14$
Multiplying $7$ by $0$ we get
$\Rightarrow -x-0=14$
By using the elementary operation, we get
$\Rightarrow -x=14$
Dividing the whole number $14$ by $(-1)$, we get
$\Rightarrow x=-14$
$\therefore y-$Intercept is $x=-14$.
Hence, we get $\therefore$$x-$ Intercept is $y=-2$
$\therefore y-$ Intercept is $x=-14$.

Note: $x-$ intercept is a point at which the graph intersects $x-axis$. That means we always have $y$ equal to zero Similarly we can say that for the $y-$intercept is a point at which the graph intersects $y-axis.$ That means we always have $x$ equal to zero in the coordinate system.
We have to know about the concept of $x-$ intercept and $y-$ intercept for a straight line, satisfying the condition of $x=0\text{ and y = 0}$ in the equation of the given line.