Given the Linear Equation:
[tex]y=-5x+2[/tex]
You can find the y-intercept and the x-intercept in order to graph it.
Notice that it is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
In this case, you can identify that the y-intercept is:
[tex]b=2[/tex]
In order to find the x-intercept, you need to substitute this value of "y" into the equation:
[tex]y=0[/tex]
Because the value of "y" is zero when the line intersects the x-axis.
Then, substituting that value and solving for "x", you get:
[tex]\begin{gathered} y=-5x+2 \\ 0=-5x+2 \\ -2=-5x \\ \\ \frac{-2}{-5}=x \\ \\ x=0.4 \end{gathered}[/tex]
Now that you know that the line passes through these points:
[tex](0.4,0),(0,2)[/tex]
You can plot them on the Coordinate Plane. See the picture below:
Finally, draw the line passing through those points.
Hence. the answer is:
