Question

Select the three equations that pass through the points (–4, –16) and (5, 2): y + 4 = 2(x – 16) y – 2 = 2(x – 5) y = 2x – 8 y + 16 = 2(x + 4

Answer 1

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

$m =\frac{2+16}{5+4}\\ m =\frac{18}{9}\\ m = 2$

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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