Question
A line passes through the origin with a slope of 2. Write the equation of this line in slope-intercept form.
Ask by Chang Potter. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = 2x \).
Solution
To write the equation of a line in **slope-intercept form**, which is:
\[
y = mx + b
\]
where:
- \( m \) is the **slope** of the line.
- \( b \) is the **y-intercept** (the point where the line crosses the y-axis).
Given:
- The line **passes through the origin** \((0, 0)\), which means the y-intercept \( b = 0 \).
- The **slope** \( m = 2 \).
Substituting these values into the slope-intercept form:
\[
y = 2x + 0
\]
Simplifying, we get:
\[
y = 2x
\]
**So, the equation of the line in slope-intercept form is:**
\[
y = 2x
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The equation of a line in slope-intercept form is expressed as \(y = mx + b\), where \(m\) represents the slope and \(b\) the y-intercept. Given that the slope is 2 and the line passes through the origin (meaning \(b = 0\)), the equation simplifies to \(y = 2x\). When graphing this line, you can start at the origin (0,0) and move up 2 units for every 1 unit you move to the right! This creates a steep, fun slope that packs a punch, giving you a line that ascends rapidly.
