Black Bird
10/24/2023 · Primary School
Find an equarion for the line blow \( (-2,2)(4,4) \)
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Tutor-Verified Answer
Step-by-step Solution
To find the equation of the line that passes through the points \((-2, 2)\) and \((4, 4)\), we can follow these steps:
1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (-2, 2)\) and \((x_2, y_2) = (4, 4)\).
Substituting the values:
\[
m = \frac{4 - 2}{4 - (-2)} = \frac{2}{4 + 2} = \frac{2}{6} = \frac{1}{3}
\]
2. **Use the point-slope form** of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
We can use either of the two points. Let's use \((-2, 2)\):
\[
y - 2 = \frac{1}{3}(x - (-2))
\]
Simplifying this:
\[
y - 2 = \frac{1}{3}(x + 2)
\]
\[
y - 2 = \frac{1}{3}x + \frac{2}{3}
\]
\[
y = \frac{1}{3}x + \frac{2}{3} + 2
\]
\[
y = \frac{1}{3}x + \frac{2}{3} + \frac{6}{3}
\]
\[
y = \frac{1}{3}x + \frac{8}{3}
\]
3. **Convert to slope-intercept form** (if needed):
The equation of the line in slope-intercept form is:
\[
y = \frac{1}{3}x + \frac{8}{3}
\]
Thus, the equation of the line that passes through the points \((-2, 2)\) and \((4, 4)\) is:
\[
y = \frac{1}{3}x + \frac{8}{3}
\]
Quick Answer
The equation of the line is \( y = \frac{1}{3}x + \frac{8}{3} \).
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