Answer:
[tex]y=-2x+6[/tex]
Step-by-step explanation:
Given:
Two points on the line are given as:
[tex](x_1,y_1)=(1,4)\\\\(x_2,y_2)=(2,2)[/tex]
Now, slope of a line passing through two points is given as:
Slope, [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the given values and solve for 'm'. This gives,
[tex]m=\dfrac{2-4}{2-1}\\\\m=\dfrac{-2}{1}=-2[/tex]
So, slope of the line is -2.
Now, the point-slope form of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]
Plug in the given values and simplify. This gives,
[tex]y-4=-2(x-1)\\\\y-4=-2x+2\\\\y=-2x+2+4\\\\y=-2x+6[/tex]
Therefore, the equation of the line is [tex]y=-2x+6[/tex]
