Complete the equation of the line through (1, 4) and (2, 2). Use exact numbers. y= Question Complete the equation of the line through (1, 4) and (2, 2). Use exact numbers. y= in progress 0 Math Jasmine 3 months 2022-02-12T02:04:35+00:00 2022-02-12T02:04:35+00:00 1 Answer 0 views 0

## Answers ( )

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]