A line in the xy-plane has a slope of 9 and passes through the point \(\mathrm{(0, -5)}\). The equation y...
GMAT Algebra : (Alg) Questions
A line in the xy-plane has a slope of 9 and passes through the point \(\mathrm{(0, -5)}\). The equation \(\mathrm{y = px + r}\) defines the line, where \(\mathrm{p}\) and \(\mathrm{r}\) are constants. What is the value of \(\mathrm{p}\)?
1. TRANSLATE the problem information
- Given information:
- Line has slope = 9
- Line passes through point \(\mathrm{(0, -5)}\)
- Equation format: \(\mathrm{y = px + r}\)
- Need to find: value of p
2. INFER what p represents in the equation
- In any linear equation \(\mathrm{y = mx + b}\):
- m = slope (coefficient of x)
- b = y-intercept
- Therefore in \(\mathrm{y = px + r}\):
- p = slope (coefficient of x)
- r = y-intercept
3. Connect the given slope to the equation
- Since the slope is 9
- And p represents the slope coefficient
- Therefore: \(\mathrm{p = 9}\)
Answer: 9
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret what p represents in the equation \(\mathrm{y = px + r}\)
Students might think p represents the y-intercept instead of the slope, especially since they're also given the point \(\mathrm{(0, -5)}\). They see that the line passes through \(\mathrm{(0, -5)}\) and incorrectly conclude that \(\mathrm{p = -5}\), thinking p is the y-intercept. This leads to confusion about the equation structure.
This causes them to get stuck and guess rather than systematically identifying coefficient roles.
The Bottom Line:
Success depends on recognizing that linear equations follow a consistent pattern regardless of the letters used - the coefficient of x is always the slope, and the constant term is always the y-intercept.