Question

How do you find the x-intercept of $4x - 3y = 12$ ?

Answer 1

We have given an equation of a line as $4x - 3y = 12$ , 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,
$4x - 3y = 12$
Now, Add $4x$ both the side ,
$\Rightarrow - 3y = 12 + 4x$
Now multiply by $- \dfrac{1}{3}$ to both the side of the equation,
$\Rightarrow y = - 4 - \dfrac{4}{3}x$
Or
$\Rightarrow y = - \dfrac{4}{3}x - 4$
Now we compare this given equation with the general linear equation i.e., $y = mx + c$
Hence ,
Slope of the given line, $m = - \dfrac{4}{3}$ .
y-intercept of the given line , $c = - 4$ .
Therefore, we can say that point $(0, - 4)$ lies on the line.
x-intercept of the given line , $\dfrac{{ - c}}{m} = \dfrac{{ - ( - 4)}}{{ - \left( {\dfrac{4}{3}} \right)}} = - 3$ .
Therefore, we can say that point $( - 3,0)$ lies on the line.

Additional Information:
i) 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 , $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ .
ii) 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 $x = 0$ .
iii) 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.