The equation $Y = 2x - 3$ represents a linear function in the slope-intercept form, which is $y = mx + b$, where:

• $m = 2$ is the slope of the line, indicating that for every unit increase in $x$, $y$ increases by 2 units.
• $b = -3$ is the y-intercept, meaning the line crosses the y-axis at $y = -3$.

Analysis:

1. Slope: The slope $2$ tells us the line rises 2 units for every 1 unit it moves to the right.
2. Y-intercept: The line crosses the y-axis at the point $(0, -3)$.
3. X-intercept: To find the x-intercept, set $Y = 0$ and solve for $x$: $0 = 2x - 3 \implies x = \frac{3}{2} = 1.5$ So, the x-intercept is at $(1.5, 0)$.

Graphing:

• The line passes through the points $(0, -3)$ and $(1.5, 0)$.
• It has a positive slope, indicating it slants upward from left to right.

Would you like more details on this equation or any specific topic?

Here are some related questions:

1. How do you find the slope of a line given two points?
2. How would the graph change if the slope were negative?
3. How do you convert a linear equation from slope-intercept to standard form?
4. What is the significance of parallel and perpendicular slopes?
5. How do you find the distance between two points on a line?

Tip: To graph a linear function quickly, find the x- and y-intercepts and plot them first, then use the slope to find additional points.