Question

How do you find the slope and intercept of $y = - 5x - 4$ ?

Answer 1

Hint : Since, we already have the equation in the slope-intercept form, we will compare it with $y = mx + c$ to find the value of $m$ as it represents as the slope of the line. Then, as we know that there are two kinds of intercepts which are $x$ -intercept and $y$ -intercept. So, $x$ -intercept is the point where the line intersects the $x$ -axis and $y$ -intercept is the point where the line intersects the $y$ -axis. So, to calculate the intercepts, we will put $x$ and $y$ as zero one by one.

Complete step-by-step answer :
(i)
We are given the line equation:
$y = - 5x - 4$
Now, since we have our equation in the slope-intercept form, we will compare the above equation with $y = mx + c$ to find the value of $m$ .
As we can see that the coefficient of $x$ is $m$ , in our equation the coefficient of $x$ is $- 5$ .
i.e.,
$m = - 5$
Therefore, the slope of the equation $y = - 5x - 4$ is $- 5$
(ii)
Now, as we know that $x$ -intercept is the point where the line crosses the $x$ -axis and we also know that on $x$ -axis, $y = 0$ . Therefore, to find the $x$ -intercept, we will put $y$ as $0$ in the equation of line given to us. Therefore,
$0 = - 5x - 4 \\\ 5x = - 4 \\\ x = - \dfrac{4}{5} \;$
Therefore, the $x$ -intercept of the equation $y = - 5x - 4$ is $- \dfrac{4}{5}$ .
(iii)
Similar to $x$ -intercept, $y$ -intercept is the point where the line crosses the $y$ -axis and we also know that on $y$ -axis, $x$ =0. Therefore, to find $y$ -intercept, we will put $x$ as $0$ in the equation of the line given to us. Therefore,
$y = - 5\left( 0 \right) - 4 \\\ y = - 4 \;$
Therefore, the $y$ -intercept of the equation $y = - 5x - 4$ is $- 4$ .

Note : A line parallel to $x$ -axis, does not intersect the $x$ -axis at any finite distance and hence, we cannot get any finite $x$ -intercept of such a line. Slope of such a line is $0$ . Similarly, lines parallel to the $y$ -axis, do not intersect $y$ -axis at any finite distance and hence, we cannot get any finite $y$ -intercept of such a line. Slope of such a line is $\infty$ .
In an equation of the form $y = mx + c$ , $m$ represents the slope of the line and $c$ represents the vertical intercept or $y$ -intercept of the line as it is the value of $y$ when $x = 0$ . Also, there is an alternative method to find the intercepts of a line equation. Convert the given line equation into intercept form of a line i.e., $\dfrac{x}{a} + \dfrac{y}{b} = 1$ , where $a$ is the $x$ -intercept and $b$ is the $y$ -intercept.