The three equations that pass through the points (–4, –16) and (5, 2) are y - 2 = 2(x - 5), y = 2x - 8 and y + 16 = 2(x+4)
Equation of a line
The equation of a line in point-slope form is expressed as:
y - y1 = m(x-x1)
- m is the slope of the line
- (x1, y1) is the point on the line
Given the coordinate points (–4, –16) and (5, 2)
Get the slope
[tex]m =\frac{2+16}{5+4}\\
m =\frac{18}{9}\\
m = 2[/tex]
Substitute m= 2 and (5, 2) into the equation to have:
y - 2 = 2(x - 5)
Expand
y - 2 = 2x - 10
y = 2x - 8
ALso using the coordinate point (-4, -16)
y - (-16) = 2(x-(-4))
y + 16 = 2(x+4)
Hence the three equations that pass through the points (–4, –16) and (5, 2) are y - 2 = 2(x - 5), y = 2x - 8 and y + 16 = 2(x+4)
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