Question:
The slope of the straight line \( \frac{x}{10} - \frac{y}{4} = 3 \) is:
The slope of the straight line \( \frac{x}{10} - \frac{y}{4} = 3 \) is:
Show Hint
For any equation in intercept form $\frac{x}{a} + \frac{y}{b} = 1$, the slope is always $-b/a$. In this problem, after adjusting the right side to 1, you can apply this ratio directly for a 5-second solution.
Updated On: May 2, 2026
- $\frac{5}{2}$
- $-\frac{5}{2}$
- $\frac{2}{5}$
- $-\frac{2}{5}$
- $\frac{3}{4}$
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The Correct Option is C
Solution and Explanation
Concept:
The slope of a line can be found by converting its general equation into the slope-intercept form $y = mx + c$, where $m$ represents the slope. Alternatively, for an equation in the form $Ax + By + C = 0$, the slope is $-A/B$.
Step 1: Rewrite the equation in general form.
The given equation is $\frac{x}{10} - \frac{y}{4} = 3$. Multiply the entire equation by the LCM of $10$ and $4$ (which is $20$) to clear fractions: \[ 20 \left( \frac{x}{10} \right) - 20 \left( \frac{y}{4} \right) = 20(3) \] \[ 2x - 5y = 60 \]
Step 2: Isolate $y$ to find the slope-intercept form.
Move $2x$ to the other side: \[ -5y = -2x + 60 \] Divide the entire equation by $-5$: \[ y = \frac{-2}{-5}x + \frac{60}{-5} \] \[ y = \frac{2}{5}x - 12 \]
Step 3: Identify the slope.
Comparing $y = \frac{2}{5}x - 12$ with $y = mx + c$, we find: \[ m = \frac{2}{5} \]
Step 1: Rewrite the equation in general form.
The given equation is $\frac{x}{10} - \frac{y}{4} = 3$. Multiply the entire equation by the LCM of $10$ and $4$ (which is $20$) to clear fractions: \[ 20 \left( \frac{x}{10} \right) - 20 \left( \frac{y}{4} \right) = 20(3) \] \[ 2x - 5y = 60 \]
Step 2: Isolate $y$ to find the slope-intercept form.
Move $2x$ to the other side: \[ -5y = -2x + 60 \] Divide the entire equation by $-5$: \[ y = \frac{-2}{-5}x + \frac{60}{-5} \] \[ y = \frac{2}{5}x - 12 \]
Step 3: Identify the slope.
Comparing $y = \frac{2}{5}x - 12$ with $y = mx + c$, we find: \[ m = \frac{2}{5} \]
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