Question:
If \(m\) and \(c\) denote the slope and the \(y\)-intercept of the line \(3x-5y-6=0\), then \((m,c)=\)
If \(m\) and \(c\) denote the slope and the \(y\)-intercept of the line \(3x-5y-6=0\), then \((m,c)=\)
Show Hint
To find the slope and intercept quickly, always convert the equation into the form
\[
y=mx+c
\]
The coefficient of \(x\) gives the slope \(m\), while the constant term gives the \(y\)-intercept \(c\).
Updated On: Jun 12, 2026
- \(\left(\dfrac{3}{5},-\dfrac{6}{5}\right)\)
- \(\left(-\dfrac{3}{5},\dfrac{6}{5}\right)\)
- \(\left(-\dfrac{3}{5},-\dfrac{6}{5}\right)\)
- \(\left(\dfrac{5}{3},2\right)\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
The standard slope-intercept form of a straight line is
\[
y = mx + c
\]
where:
• \(m\) represents the slope (gradient) of the line.
• \(c\) represents the \(y\)-intercept, i.e., the point where the line cuts the \(y\)-axis. To find the values of \(m\) and \(c\), we first convert the given equation into slope-intercept form. Step-by-Step Solution:
• The given equation of the line is \[ 3x-5y-6=0 \]
• Rearrange the equation to isolate \(y\): \[ -5y=-3x+6 \]
• Divide the entire equation by \(-5\): \[ y=\frac{-3x+6}{-5} \] \[ y=\frac{3}{5}x-\frac{6}{5} \]
• Compare this equation with the standard form \[ y=mx+c \] \[ m=\frac{3}{5}, \qquad c=-\frac{6}{5} \]
• Therefore, \[ (m,c)=\left(\frac{3}{5},-\frac{6}{5}\right) \] Hence, the correct answer is \[ \boxed{\left(\frac{3}{5},-\frac{6}{5}\right)} \]
• \(m\) represents the slope (gradient) of the line.
• \(c\) represents the \(y\)-intercept, i.e., the point where the line cuts the \(y\)-axis. To find the values of \(m\) and \(c\), we first convert the given equation into slope-intercept form. Step-by-Step Solution:
• The given equation of the line is \[ 3x-5y-6=0 \]
• Rearrange the equation to isolate \(y\): \[ -5y=-3x+6 \]
• Divide the entire equation by \(-5\): \[ y=\frac{-3x+6}{-5} \] \[ y=\frac{3}{5}x-\frac{6}{5} \]
• Compare this equation with the standard form \[ y=mx+c \] \[ m=\frac{3}{5}, \qquad c=-\frac{6}{5} \]
• Therefore, \[ (m,c)=\left(\frac{3}{5},-\frac{6}{5}\right) \] Hence, the correct answer is \[ \boxed{\left(\frac{3}{5},-\frac{6}{5}\right)} \]
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