Question

How do you find the x-intercept and y-intercept of $7x + 8y = 18$ ?

Answer 1

We have given an equation of a line as $7x + 8y = 18$, which is a straight-line equation. A straight-line equation is always linear and represented as $y = mx + c$ where $m$ is the slope of the line and $c$ is the y-intercept and $\dfrac{{ - c}}{m}$ is the x-intercept.

Complete step by step solution:
We have equation of line,
$7x + 8y = 18$
Now, subtract $7x$ from both the side ,
$\Rightarrow 8y = 18 - 7x$
Now multiply by $\dfrac{1}{8}$ to both the side of the equation,
$\Rightarrow y = \dfrac{{18}}{8} - \dfrac{7}{8}x$
Or
$\Rightarrow y = - \dfrac{7}{8}x + \dfrac{{18}}{8}$
Now we compare this given equation with the general linear equation i.e., $y = mx + c$
Hence ,
Slope of the given line, $m = - \dfrac{7}{8}$ .
y-intercept of the given line , $c = \dfrac{{18}}{8}$ .
Therefore, we can say that the point $\left( {0,\dfrac{{18}}{8}} \right)$ lie on the line.
x-intercept of the given line , $\dfrac{{ - c}}{m} = \dfrac{{ - \left( {\dfrac{{18}}{8}} \right)}}{{ - \left( {\dfrac{7}{8}} \right)}} = \dfrac{{18}}{7}$ .

Therefore, we can say that the point $\left( {\dfrac{{18}}{7},0} \right)$ lies on the line.

Additional Information:
Slope of a line can also be found if two points on the line are given . let the two points on the line be $({x_1},{y_1}),({x_2},{y_2})$ respectively.
Then the slope is given by, $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$.
Slope is also defined as the ratio of change in $y$ over the change in $x$ between any two points.
y-intercept can also be found by substituting $x = 0$.
Similarly, x-intercept can also be found by substituting $y = 0$.

Note:
This type of linear equation is sometimes called slope-intercept form because we can easily find the slope and the intercept of the corresponding lines. This also allows us to graph it.
We can quickly tell the slope i.e., $m$ the y-intercepts i.e., $(y,0)$ and the x-intercept i.e., $(0,y)$. we can graph the corresponding line .