Parsons John
12/10/2023 · Middle School
Write the equation of a line in slope-intercept form that passes through the point (1, 2) with a slope of 3.
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Step-by-step Solution
To write the equation of a line in slope-intercept form, which is given by the formula:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and the point through which the line passes.
Given:
- Slope (\( m \)) = 3
- Point = (1, 2)
We can substitute the slope and the coordinates of the point into the equation to find \( b \):
1. Substitute \( m = 3 \), \( x = 1 \), and \( y = 2 \) into the equation:
\[
2 = 3(1) + b
\]
2. Simplify the equation:
\[
2 = 3 + b
\]
3. Solve for \( b \):
\[
b = 2 - 3
\]
\[
b = -1
\]
Now that we have the slope and the y-intercept, we can write the equation of the line:
\[
y = 3x - 1
\]
Thus, the equation of the line in slope-intercept form is:
\[
y = 3x - 1
\]
Quick Answer
The equation of the line is \( y = 3x - 1 \).
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