The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line?

-4 is your slope and -8 is your y-intercept. The standard slope intercept formula is y = mx+b where m is your slope, b is your y-intercept, and x and y are x and y. All you have to do is plug in your variables and you are left with y = -4x-8

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ColinJacobus ColinJacobus · Answer 2 · 2019-06-17T15:43:19+02:00

Answer: The required slope-intercept form of the given line is

[tex]y=\dfrac{1}{4}x+2.[/tex]

Step-by-step explanation: Given that the point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is as follows :

[tex]y-4=\dfrac{1}{4}(x-8)~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the slope-intercept form of the equation (i).

We know that

the slope-intercept form of the equation of a straight line with slope m and y-intercept c is given by

[tex]y=mx+c.[/tex]

From equation (i), we have

[tex]y-4=\dfrac{1}{4}(x-8)\\\\\\\Rightarrow y-4=\dfrac{1}{4}x-2\\\\\\\Rightarrow y=\dfrac{1}{4}x-2+4\\\\\\\Rightarrow y=\dfrac{1}{4}x+2.[/tex]

Thus, the required slope-intercept form of the given line is

[tex]y=\dfrac{1}{4}x+2.[/tex]