Answer:
[tex]y=-2x+10[/tex] represents the line of best fit for the scatter plot. The graph of [tex]y=-2x+10[/tex] is also attached below.
Step-by-step explanation:
Considering the equation
[tex]y=-2x+10[/tex]
[tex]\mathrm{x-intercept\:is\:a\:point\:on\:the\:graph\:where\:}y=0[/tex]
[tex]-2x+10=0[/tex]
[tex]-2x+10-10=0-10[/tex]
[tex]\frac{-2x}{-2}=\frac{-10}{-2}[/tex]
[tex]x=5[/tex]
so,
[tex]x-\mathrm{axis\:interception\:points\:of\:}-2x+10:\quad \left(5,\:0\right)[/tex]
[tex]y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0[/tex]
[tex]y=-2\cdot \:0+10[/tex]
[tex]y=-0+10[/tex]
[tex]y=10[/tex]
so,
[tex]y-\mathrm{axis\:interception\:point\:of\:}-2x+10:\quad \left(0,\:10\right)[/tex]
Thus,
[tex]\mathrm{X\:Intercepts}:\:\left(5,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:10\right)[/tex]
also
[tex]\mathrm{Slope\:of\:}-2x+10:\quad m=-2[/tex]
Therefore, [tex]y=-2x+10[/tex] represents the line of best fit for the scatter plot.
The graph of [tex]y=-2x+10[/tex] is also attached below. From the graph, it is clear that it very much fits for the scatter plot.
