Question

How do you find the x-intercept and y-intercept of $5x - 6y = 30$ ?

Answer 1

We have given an equation of a line as $5x - 6y = 30$ , 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,
$\Rightarrow 5x - 6y = 30$
Now, subtract $5x$ from both the side ,
$\Rightarrow - 6y = 30 - 5x$
Now multiply by $- \dfrac{1}{6}$ to both the side of the equation,
$\Rightarrow y = - 5 + \dfrac{5}{6}x$
Or
$\Rightarrow y = \dfrac{5}{6}x - 5$
Now we compare this given equation with the general linear equation i.e., $y = mx + c$
Hence ,
Slope of the given line, $m = \dfrac{5}{6}$ .
y-intercept of the given line , $c = - 5$ .
Therefore, we can say that point $(0, - 5)$ lie on the line.
x-intercept of the given line , $\dfrac{{ - c}}{m} = \dfrac{{ - ( - 5)}}{{\left( {\dfrac{5}{6}} \right)}} = 6$ .
Therefore, we can say that point $(6,0)$ lie 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 equations 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 .