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 plus 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 minus 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 the point the line passes through, and \(m\) is the slope.

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

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

Now substitute these values into the point-slope formula:

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

Thus, the point-slope form of the equation is:

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

So, the correct answer from the options provided is:

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