Versions of Linear Equations Quick Check

Question

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Question
Write the linear equation in point-slope form given a line that passes through the point (−14,8)
and has a slope of −3
.(1 point)
Responses

y−8=−3(x+14)
y minus 8 equals negative 3 left parenthesis x plus 14 right parenthesis

y−8=−3(x−14)
y minus 8 equals negative 3 left parenthesis x minus 14 right parenthesis

y+8=−3(x+14)
y plus 8 equals negative 3 left parenthesis x plus 14 right parenthesis

y+8=3(x+14)

Answer 1

To write the linear equation in point-slope form, we use the formula:

\[ y - y_1 = m(x - x_1) \]

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

Given the point \( (-14, 8) \) and the slope \( -3 \):

• \( x_1 = -14 \)
• \( y_1 = 8 \)
• \( m = -3 \)

Substituting these values into the formula, we get:

\[ y - 8 = -3(x - (-14)) \]

This simplifies to:

\[ y - 8 = -3(x + 14) \]

So the point-slope form of the equation is:

\( y - 8 = -3(x + 14) \)

The correct response is:

y−8=−3(x+14)