Goodwin Fitzgerald
07/11/2023 · Senior High School
Find the equation (in terms of \( x \) ) of the line through the points \( (-4,-4) \) and \( (1,6) \) \( y=\square \)
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Step-by-step Solution
To find the equation of the line through the points \((-4, -4)\) and \((1, 6)\), we first need to calculate the slope \(m\) of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (-4, -4)\) and \((x_2, y_2) = (1, 6)\). Plugging in these values:
\[
m = \frac{6 - (-4)}{1 - (-4)} = \frac{6 + 4}{1 + 4} = \frac{10}{5} = 2
\]
Now that we have the slope \(m = 2\), we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-4, -4)\) and the slope \(m = 2\):
\[
y - (-4) = 2(x - (-4))
\]
This simplifies to:
\[
y + 4 = 2(x + 4)
\]
Now, distribute the \(2\):
\[
y + 4 = 2x + 8
\]
Next, we isolate \(y\) by subtracting \(4\) from both sides:
\[
y = 2x + 8 - 4
\]
This simplifies to:
\[
y = 2x + 4
\]
Thus, the equation of the line in terms of \(x\) is:
\[
\boxed{y = 2x + 4}
\]
Quick Answer
The equation of the line is \( y = 2x + 4 \).
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