Find the slope and the y-intercept of the line 2x - 5y = -15. Then use them to graph the line.
Understand the Problem
The question asks to find the slope and y-intercept of the line given by the equation 2x - 5y = -15, and then use these values to plot/graph the line. The equation needs to be converted to slope-intercept form (y = mx + b) to easily identify the slope (m) and y-intercept (b).
Answer
slope: $\frac{2}{5}$ y-intercept: $3$
Answer for screen readers
slope: $\frac{2}{5}$ y-intercept: $3$
Steps to Solve
- Convert the equation to slope-intercept form
The given equation is $2x - 5y = -15$. To convert it to slope-intercept form ($y = mx + b$), we need to isolate $y$ on one side of the equation.
- Isolate the y term
Subtract $2x$ from both sides of the equation:
$2x - 5y - 2x = -15 - 2x$
$-5y = -2x - 15$
- Solve for y
Divide both sides of the equation by $-5$:
$\frac{-5y}{-5} = \frac{-2x - 15}{-5}$
$y = \frac{-2x}{-5} + \frac{-15}{-5}$
$y = \frac{2}{5}x + 3$
- Identify the slope and y-intercept
Now that the equation is in slope-intercept form ($y = mx + b$), we can identify the slope ($m$) and the y-intercept ($b$).
The slope, $m$, is the coefficient of $x$, which is $\frac{2}{5}$.
The y-intercept, $b$, is the constant term, which is $3$.
slope: $\frac{2}{5}$ y-intercept: $3$
More Information
The slope-intercept form of a linear equation is $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept. The slope indicates the steepness and direction of the line, while the y-intercept is the point where the line crosses the y-axis.
Tips
A common mistake is not dividing both terms on the right side of the equation by $-5$. Remember to divide both $-2x$ and $-15$ by $-5$. Also, forgetting the negative sign is a common mistake.
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