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The equations are written in point-slope form. Which equation represents a line through points (–8, 3) and (–2, –3)?

y-3=-3(x+8)
y-3=3(x+8)
y-3=1(x+8)
y-3=-1(x+8)

Respuesta :

texaschic101
(-8,3)(-2,-3)
slope(m) = (-3-3) / (-2 - (-8) = -6/6 = -1

y - y1 = m(x - x1)
slope(m) = -1
(-8,3)...x1 = -8 and y1 = 3
now we sub
y - 3 = -1(x - (-8) =
y - 3 = -1(x + 8)

Answer:

Option 4th is correct

[tex]y-3 = -1(x+8)[/tex]

Step-by-step explanation:

Point-slope intercept form:

The equation of  straight line is given by:

[tex]y-y_1 = m(x-x_1)[/tex] .....[1]

where, m is the slope and [tex](x_1, y_1)[/tex] is the point on the line.

As per the statement:

A line through points (–8, 3) and (–2, –3).

Formula for slope is given by:

[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points we have;

[tex]m = \frac{-3-3}{-2-(-8)} = \frac{-6}{-2+8}=\frac{-6}{6} = -1[/tex]

Substitute the given value of m = -1 and (-8, 3) in [1] we have;

[tex]y-3 = -1(x-(-8))[/tex]

⇒[tex]y-3 = -1(x+8)[/tex]

Therefore, the equations represents a line through points (–8, 3) and (–2, –3) is, [tex]y-3 = -1(x+8)[/tex]