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

Question

bsplit2001 bsplit2001

04-11-2026
Mathematics

Answered

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

Verified Answer :

Related Questions

Given a regular polygon with five sides how many congruent triangles can you dissect the polygon into using the center point and two adjacent vertices of the po

What are the five factors of 7

The length of a rectangle is 4 cm longer than its width If the perimeter of the rectangle is 40 cm find its area

Read the excerpt below from Life of Caesar by Plutarch and answer the question that follows At Rome moreover Caesar won a great and brilliant popularity by his

how many atoms are in 350 moles of calcium ca

The population shift from China occurred during the years of the Song dynasty eastern to western western to eastern northern to southern southern to northern

Early Christians were persecuted for their beliefs Which beliefs in particular made others often suspicious of Christians

ضع علامة الترقيم المناسبة في الفراغ الموجود بين كل قوسين في النص التالي الصحة من أجل النعم التي أنعم الله تعالى بها على الإنسان وأرفعها مقاما إذ بها يطيب العيش

what percent of 96 is 36 step by step

The formula gives the height h ab of a parallelogram with area A and base b What is the height of a parallelogram with an area of 78 cm2 and a base of 13 cm

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T15:49:30-05:00

The equation $y = -\frac{3}{2}x - 3$ is in slope-intercept form, with slope $m = -\frac{3}{2}$ and y-intercept $b = -3$.
The line passes through the points $(0, -3)$, $(2, -6)$, and $(-2, 0)$.
Plot these points on the coordinate plane and connect them with a straight line.
The resulting line represents a constant downward rate of change of 1.5 units per 1 horizontal unit.

Explanation

Analyzing the Linear Equation

The equation $y = -\frac{3}{2}x - 3$ represents a linear function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope $m = -\frac{3}{2}$ and the y-intercept $b = -3$. The y-intercept indicates that the line passes through the point $(0, -3)$ on the Cartesian coordinate plane.

Identifying Points on the Line

To graph this line, we need to find at least two points that satisfy the equation. We already have the y-intercept $(0, -3)$. To find another point, we can choose a convenient value for $x$. Let's pick $x = 2$. Substituting this into the equation, we get:
\[y = -\frac{3}{2}(2) - 3 = -3 - 3 = -6.\]
So, the point $(2, -6)$ lies on the line. We can also pick $x = -2$:
\[y = -\frac{3}{2}(-2) - 3 = 3 - 3 = 0.\]
Thus, the point $(-2, 0)$ is also on the line. These three points, $(-2, 0)$, $(0, -3)$, and $(2, -6)$, confirm the trajectory of the line.

Understanding the Slope

The slope $m = -\frac{3}{2}$ represents the rate of change of $y$ with respect to $x$. It tells us that for every 2 units we move to the right along the x-axis, the line moves 3 units downward. Starting at the y-intercept $(0, -3)$, moving right 2 units brings us to $x=2$, and moving down 3 units brings us to $y=-6$, confirming our point $(2, -6)$. This constant slope ensures that the graph is a straight line.

Drawing the Graph

To draw the graph, plot the points $(-2, 0)$, $(0, -3)$, and $(2, -6)$ on a coordinate system. Using a straight edge, draw a line passing through these points. Since it is a linear function, the line extends infinitely in both directions. The graph displays a downward slope, reflecting the negative value of $m$. The final visual representation is a straight line crossing the y-axis at $-3$ and the x-axis at $-2$.

Examples

Understanding how to graph linear equations is fundamental in various real-life scenarios, such as modeling costs over time or calculating depreciation. For example, if a company's equipment value decreases linearly over time, the equation $V = -mt + V_0$ can predict the value $V$ at any time $t$. Mastering the slope-intercept form allows you to easily visualize these trends and make informed decisions based on the rate at which values change.