Question

How do you graph the equation $y=-\dfrac{3}{4}x-1$?

Answer 1

We are asked to draw the graph of the equation $y=-\dfrac{3}{4}x-1$. The degree of an equation is the highest power of the variable present in it. So, for this equation, the highest power present $x$ is 1, the degree is also 1. From this, it can be said that this is a linear equation. The graph of a linear equation represents a straight line.

Complete step by step answer:
The general equation of a straight line is $ax+by+c=0$, where $a,b,c$ are any real numbers. The given equation is $y=-\dfrac{3}{4}x-1$, the equation can also be written as $\dfrac{3}{4}x+1+y=0$, comparing with the general equation of straight line, we get $a=\dfrac{3}{4},b=1\And c=1$.
To plot the graph of an equation of the straight line, we should know at least two points, through which the line passes.
To make things simple, let’s take the X-intercept and Y-intercept as the two points. X-intercept is the point where the line crosses X-axis, this means that the Y-coordinate will be $0$, similarly, Y-intercept is the point where the line crosses Y-axis, so X-coordinate will be $0$. We will use this property now.
We substitute $y=0$ in the equation $\dfrac{3}{4}x+1+y=0$, we get

& \Rightarrow \dfrac{3}{4}x+1+0=0 \\\ & \Rightarrow \dfrac{3}{4}x+1=0 \\\ \end{aligned}$$ Subtracting 1 from both sides of equation we get, $$\begin{aligned} & \Rightarrow \dfrac{3}{4}x+1-1=0-1 \\\ & \Rightarrow \dfrac{3}{4}x=-1 \\\ \end{aligned}$$ We multiply $$\dfrac{4}{3}$$ to both sides we get, $$\begin{aligned} & \Rightarrow \left( \dfrac{3}{4}x \right)\times \dfrac{4}{3}=\left( -1 \right)\times \dfrac{4}{3} \\\ & \therefore x=\dfrac{-4}{3} \\\ \end{aligned}$$ So, the coordinates of the X-intercept are $$\left( \dfrac{-4}{3},0 \right)$$. Similarly, now we substitute $$x=0$$ in the equation $$5x-y-5=0$$, we get $$\Rightarrow \dfrac{3}{4}\left( 0 \right)+1+y=0$$ Adding $$-1$$ to both sides of the equation, we get $$\begin{aligned} & \Rightarrow 1+y-1=0-1 \\\ & \therefore y=-1 \\\ \end{aligned}$$ So, the coordinates of the Y-intercept are$$\left( 0,-1 \right)$$. Using these two points we can plot the graph of the equation as follows:  **Note:** Here, we found the two points which are X-intercept and Y-intercept by substituting either-or $$y$$, one at a time. We can also find these values by converting the straight-line equation to the equation in intercept form which is, $$\dfrac{x}{a}+\dfrac{y}{b}=1$$. Here, $$a\And b$$are X-intercept and Y-intercept respectively.