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
Jasmine 3 months 2022-02-12T02:04:35+00:00 1 Answer 0 views 0

Answers ( )

    0
    2022-02-12T02:05:43+00:00

    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]

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )