Question

How do you write an equation of line with slope of line being -1 and y-intercept 0?

Answer 1

In the above type of questions where we know the value of slope of the equation and also the y-intercept we will use the slope form of equation which is basically y=mx+b, there are many other ways to find the slope of the equation but to find it fast and in easier way we will be using the slope form of equation.

Complete step by step answer:
In the above mentioned question we are given the slope of the line and also the y-intercept of the line. Before we proceed, the meaning of y-intercept is the value of y when the value of x is zero (0). We will be using both the given values to find the equation of the line. To find the equation of line we will first proceed with the slope form of the equation as it has already been mentioned in the question so to calculate a faster and easier way we will use the slope form of line equation.
The slope of form of line equation is: y=mx+b, in this equation the value of m is the slope and b is a constant now that we know the value of slope we will use it to find the first part of the equation and we get it as:
$\Rightarrow y=-x+b$
Now to calculate the constant part of the equation we will use the y-intercept value. To use the y-intercept we will substitute x=0 and then substitute y with y-intercept which will give us the value of constant i.e.

& \Rightarrow 0=0+b \\\ & \Rightarrow 0=b \\\ \end{aligned}$$ So we got the value of constant as zero (0) with which we will substitute in the equation which will provide us with our equation of line that was required: $$\begin{aligned} & \Rightarrow y=-x+0 \\\ & \Rightarrow y=-x \\\ \end{aligned}$$ So the final equation of line is $$y=-x$$  **Note:** In the above mentioned question we know that there are many ways to solve this question but as the slope was given we used this formula to solve it faster and easier, there are different forms of line equation which can be used so having a basic idea of when to use what will be beneficial.