Guerrero Mcdonald
05/02/2024 · High School
The slope and one point on the line are given. Find the equation of the line (in slope-intercept form). \( (-1,5) ; m=1 \)
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Tutor-Verified Answer
Step-by-step Solution
To find the equation of the line in slope-intercept form \(y = mx + b\), we can use the given point \((-1, 5)\) and the slope \(m = 1\).
1. Start with the slope-intercept form:
\[
y = mx + b
\]
2. Substitute the slope \(m = 1\):
\[
y = 1x + b \quad \text{or} \quad y = x + b
\]
3. Now, use the point \((-1, 5)\) to find \(b\). Substitute \(x = -1\) and \(y = 5\) into the equation:
\[
5 = (-1) + b
\]
4. Solve for \(b\):
\[
5 = -1 + b \\
b = 5 + 1 \\
b = 6
\]
5. Now, substitute \(b\) back into the equation:
\[
y = x + 6
\]
Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = x + 6}
\]
Quick Answer
The equation of the line is \(y = x + 6\).
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