Question

How does one can plot the graph $y = 5 - 2x$?

Answer 1

Hint: We have given an equation of a line as $y = 5 - 2x$ , which is a straight-line equation. A straight-line equation is always linear and represented as $y = mx + c$ where $m$is the slope of the line and $c$ is the y-intercept and $\dfrac{{ - c}}{m}$ is the x-intercept .

Complete step by step solution:
We have equation of line,
 $
  y = 5 - 2x \\
  or \\
  y = - 2x + 5 \\
 $
Now we compare this given equation with the general linear equation i.e., $y = mx + c$
Hence ,
Slope of the given line, $m = - 2$ .
y-intercept of the given line , $c = 5$ .
Therefore, we can say that point $(0,5)$ lie on the line.
x-intercept of the given line , $\dfrac{{ - c}}{m} = \dfrac{{ - 5}}{{ - 2}} = \dfrac{5}{2}$ .
Therefore, we can say that point $(\dfrac{5}{2},0)$ lie on the line.
With the help of two points, we can plot the graph by connecting the points as follow,

Note: This type of linear equations sometimes called slope-intercept form because we can easily find the slope and the intercept of the corresponding lines. This also allows us to graph it.
We can quickly tell the slope i.e., $m$ the y-intercepts i.e., $(y,0)$ and the x-intercept i.e., $(0,y)$ .we can graph the corresponding line .