Question
A line with a slope of 2 passes through the point (9,
–
2). What is its equation in point-slope form?
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2). What is its equation in point-slope form?
Answers
GPT-4o mini
To write the equation of a line in point-slope form, we use the formula:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \((x_1, y_1)\) is the point the line passes through.
Here, the slope \( m \) is 2 and the point is \((9, -2)\). Plugging in these values, we have:
\[
y - (-2) = 2(x - 9)
\]
This simplifies to:
\[
y + 2 = 2(x - 9)
\]
So, the equation of the line in point-slope form is:
\[
y + 2 = 2(x - 9)
\]
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \((x_1, y_1)\) is the point the line passes through.
Here, the slope \( m \) is 2 and the point is \((9, -2)\). Plugging in these values, we have:
\[
y - (-2) = 2(x - 9)
\]
This simplifies to:
\[
y + 2 = 2(x - 9)
\]
So, the equation of the line in point-slope form is:
\[
y + 2 = 2(x - 9)
\]