The equation $3x + 5 = y$ is a linear equation in two variables, $x$ and $y$. Let's analyze it:

General Form

The general form of a linear equation in two variables is: $Ax + By + C = 0$ or $y = mx + b$ where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

Your equation is already in slope-intercept form:
$y = 3x + 5$

Key Details

1. Slope ($m$): The coefficient of $x$ is $3$, so the slope is $3$. This means the line rises $3$ units vertically for every $1$ unit it moves horizontally.
2. Y-intercept ($b$): The constant term $5$ is the y-intercept. The line crosses the y-axis at $(0, 5)$.
3. X-intercept: To find the x-intercept, set $y = 0$: $0 = 3x + 5 \implies x = -\frac{5}{3}$ The line crosses the x-axis at $\left(-\frac{5}{3}, 0\right)$.
4. Graph: The line passes through $(0, 5)$ and has a steep positive slope.

Would you like a graph or a step-by-step explanation of any of these points?

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Related Questions

1. What is the meaning of the slope $m = 3$ in a practical context?
2. How do you find the distance between two points on the line $y = 3x + 5$?
3. How does changing the slope or y-intercept affect the graph of the equation?
4. What are parallel and perpendicular lines to $y = 3x + 5$?
5. How can you write this equation in standard form?

Tip

To quickly sketch a line, plot the y-intercept first, then use the slope to find additional points. For example, starting at $(0, 5)$, move up 3 units and right 1 unit to locate another point.