The equation for the mentioned set of points (2, -8), (6, 10) will be as follows:
Remember the slope-intercept equation: y = mx = b
To solve this, first we will need to calculate the slope and y-intercept (b).
Equation for slope (m) is,
[tex]m =\frac{ (y_{2} - y_{1})}{(x_{2} - x_{1})}[/tex]
= [tex]\frac{10 - (-8)}{6-2}[/tex] = [tex]\frac{18}{4}[/tex] = [tex]\frac{9}{2}[/tex] = 4.5
Now, to write an equation for a line,
y = mx + b
where,
m = slope
b = y-intercept
So,
y = 4.5x + b
Putting the values of (x,y) = (6,10) to get the y-intercept,
10 = (4.5 x 6) + b
So, b = 10 - 27 = -17
Hence, the equation of line will be,
y = 4.5x - 17
or, y - 4.5x = -17
or, 4.5x - y = 17
or, 9x - 2y = 34
So, the correct equation for the mentioned two points will be 9x - 2y = 34.
Learn more about linear equation here:
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