Graph $y=-\frac{3}{2} x-3$.

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bsplit2001 bsplit2001

04-11-2026
Mathematics

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Graph $y=-\frac{3}{2} x-3$.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T15:48:07-05:00

Identify the slope $m = -\frac{3}{2}$ and y-intercept $b = -3$ from the equation $y = -\frac{3}{2}x - 3$.
Calculate two points on the line: when $x=0$, $y=-3$; when $x=2$, $y=-6$.
Draw a straight line through the points $(0, -3)$ and $(2, -6)$.
Recognize that the negative slope indicates the line slants downwards from left to right.

The equation represents a line passing through $\boxed{(0, -3)}$ and $\boxed{(2, -6)}$.

Explanation

Analyzing the Linear Equation

The given linear equation is $y = -\frac{3}{2}x - 3$. This equation is in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, the slope $m = -\frac{3}{2}$ and the y-intercept $b = -3$. This tells us that the graph is a straight line that crosses the y-axis at the point $(0, -3)$ and has a steepness dictated by its slope. A slope of $-\frac{3}{2}$ means that for every 2 units we move to the right along the x-axis, the line moves 3 units downward.

Finding Points to Graph the Line

To graph the line, we identify at least two points that satisfy the equation.
First, we find the y-intercept by setting $x = 0$:
\[y = -\frac{3}{2}(0) - 3 = -3\]
This gives us the point $(0, -3)$.
Next, we pick another value for $x$. Let's choose $x = 2$:
\[y = -\frac{3}{2}(2) - 3 = -3 - 3 = -6\]
This gives us the point $(2, -6)$.
Connecting these two points, $(0, -3)$ and $(2, -6)$, allows us to draw the graph of the entire line.

Describing the Graph

The graph of the equation $y = -\frac{3}{2}x - 3$ is a straight line passing through the points $(0, -3)$ and $(2, -6)$. Because the slope is negative, the line slants downwards from left to right. Since the slope is $-\frac{3}{2}$, it passes through any points $(x, y)$ such that $y$ decreases by 3 for every 2-unit increase in $x$. This line extends infinitely in both directions.

Examples

In economics, linear equations are frequently used to model demand curves. For instance, if the relationship between the price of an item ($x$) and the quantity demanded ($y$) can be represented by a line such as $y = -\frac{3}{2}x - 3$, a business can use this graph to visualize how changing the price affects sales volume. By plotting such a line, you can easily identify the expected demand at any given price point, helping you make informed decisions about pricing strategies to maximize revenue.