Question

How do you find the slope given $y = - 3x + 5$ ?

Answer 1

Here in this question, give the linear equation. We have to find the slope of a given linear equation. Generally, the slope intercept form is $y = mx + c$ where m is the slope of the line and c is the y intercept. So, we can compare with standard form to get the slope and intercept of the given linear equation.

Complete step-by-step solution:
The given equation is a linear equation. These equations are defined for lines in the coordinate
system. An equation for a straight line is called a linear equation i.e., $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. Occasionally, this equation is called a “linear equation of two
variables” where y and x are the variables. The general or standard representation of the straight-
the line equation is $Ax + By = C$, it involves only a constant term and a first-order (linear) term.
Consider the given equation
$\Rightarrow \,\,\,y = - 3x + 5$
First, we will check whether it is in standard form i.e., $y = mx + c$ or not. is not then we will arrange the terms so that it is in standard form and then compare.
But here it is already in standard form. So we will compare directly with the standard form of slope intercept.
Hence, the slope of given graph is clearly we can say as
$\Rightarrow \,\,m = - 3$.
The slope of the linear equation $y = - 3x + 5$ represented in the graph as:

Note: Note that writing the given equation in slope intercept form is simply a procedure of steps to be followed. If we are given two points of coordinate system lying on a line then we also can find the slope of the line. That equation involves slope and intercept.