Question

How do you find the x-intercept and y-intercept of $y = - 9x$ ?

Answer 1

We have given an equation of a line as $y = - 9x$ , 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,
$y = - 9x$
We can write it as ,
$y = - 9x + 0$
Now we compare this given equation with the general linear equation i.e., $y = mx + c$
Hence ,
Slope of the given line, $m = - 9$ .
y-intercept of the given line , $c = 0$ .
Therefore, we can say that point $(0,0)$ lies on the line.
x-intercept of the given line , $\dfrac{{ - c}}{m} = \dfrac{{ - 0}}{{ - 9}} = 0$ .
Therefore, we can say that point $(0,0)$ 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 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 .