Question

The equation is: $y = - 3x - 5$ . What is the slope? What is the $y -$ intercept?

Answer 1

In the above question, we have been given an equation. And we have to find the slope and $y -$ intercept.
So we will compare the given equation with the slope intercept form of the equation of line.
Slope intercept form of line having slope $'m'$ and the $y -$ intercept equals to $'b'$ .
The general form is:
$y = mx + b$.

Complete step by step answer:
Here we have an equation:
$y = - 3x - 5$ .
We should first understand their meaning in order to find the value of slope and $y -$ intercept.
The change of $y -$ value over the change of $x -$ value is known as the slope of line. It is also known as the gradient of the line. We can also call it ‘Rise over run’.
Now the intercept of a line is the point where the line touches the $x$ or $y$ axis.
Let us write the slope intercept form:
$y = mx + b$, where $m$ is the slope and $b$ is the $y -$ intercept.
By comparing this from the given equation, we have
$m = - 3$ and the value of $b = - 5$ .
Hence the slope of the given equation is $- 3$ and the $y -$intercept is $- 5$ .

Note:
We should know that if the value of constant i.e. $b = 0$, then it means that the line will pass through the origin and will have values of $x$ and $y$ intercepts equal.
The above slope intercept form is of the straight line.
We should also know the standard form of a linear equation i.e.
$Ax + By = C$ , where $A,B$ are the constants.