Question

How do you find the slope of a line with x-intercept 3 and y-intercept -4?

Answer 1

We must have a prior knowledge of the various forms of equation line, especially the slope intercept form and the intercept forms. We are given the x-intercept and y-intercept of a line, therefore, we must first write the intercept form equation of the given line. Further we will rearrange the terms and convert it into the slope intercept form of line to find the slope.

Complete step-by-step answer:
The x-intercept is the distance from origin of the point on the given function where the value of y is zero. This point logically lies on the x-axis and is given as $\left( a,0 \right)$ where $a$ is called the x-intercept.
The y-intercept is the distance from origin of the point on the given function where the value of x is zero. This point logically lies on the y-axis and is given as $\left( 0,b \right)$ where $b$ is called the y-intercept.
The equation of a straight line is expressed especially in an intercept form which is given as $\dfrac{x}{a}+\dfrac{y}{b}=1$ where $a$ is the x-intercept of line and $b$ is the y-intercept of the line as mentioned before. One essential feature of the intercept form of line is that its constant term is always equal to 1.
Therefore, the intercept equation of line is $\dfrac{x}{3}+\dfrac{y}{\left( -4 \right)}=1$.
On multiplying the equation with 12 and rearranging, we get
$\Rightarrow \left( 12 \right)\dfrac{x}{3}+\left( 12 \right)\dfrac{y}{\left( -4 \right)}=\left( 12 \right)1$
$\Rightarrow 4x-3y=12$
Now, taking the y term to the right-hand side and dividing the equation 3, we get
$\begin{aligned} & \Rightarrow 4x-12=3y \\\ & \Rightarrow \dfrac{4x}{3}-\dfrac{12}{3}=\dfrac{3y}{3} \\\ & \Rightarrow \dfrac{4}{3}x-4=y \\\ \end{aligned}$
The slope-intercept form of a line is expressed as:
$y=mx+c$
Where,
$m=$ slope of line
$c=$ intercept of the line
Therefore, on comparing with the slope intercept form of line, $y=mx+c$,
We get $m=\dfrac{4}{3}$
Therefore, the slope of the given line is equal to $\dfrac{4}{3}$.

Note:
The coefficient of x-variable is the slope of the line in the slope-intercept form of the equation of line. We must take care that the coefficient of y-variable is always 1 in the slope-intercept form of a straight line. Therefore, we must divide the entire equation with the coefficient of y to make it equal to one.