Graphing Linear Equations Worksheet featuring six equations to plot on coordinate planes.

Here are the steps to graph each linear equation on the coordinate plane.

1) $y = -4$

* Type: Horizontal Line.
* Reasoning: The equation says that $y$ is always $-4$, no matter what $x$ is.
* How to Graph: Find $-4$ on the vertical y-axis. Draw a straight horizontal line across the entire grid at that level. It passes through points like $(0, -4)$, $(2, -4)$, and $(-5, -4)$.

2) $y = 2x + 3$

* Type: Slanted Line (Slope-Intercept Form).
* Y-intercept ($b$): $+3$. Start by plotting a point at $(0, 3)$ on the y-axis.
* Slope ($m$): $2$ (which is $\frac{2}{1}$). This means "rise 2, run 1".
* How to Graph:
1. Plot the point $(0, 3)$.
2. From there, go up 2 units and right 1 unit to plot the next point at $(1, 5)$.
3. Go back to $(0, 3)$, go down 2 units and left 1 unit to plot a point at $(-1, 1)$.
4. Connect these points with a straight line.

3) $x + y = 6$

* Type: Slanted Line (Standard Form).
* Strategy: Find the intercepts (where the line crosses the axes).
* X-intercept: Set $y = 0$. Then $x + 0 = 6$, so $x = 6$. Plot point $(6, 0)$.
* Y-intercept: Set $x = 0$. Then $0 + y = 6$, so $y = 6$. Plot point $(0, 6)$.
* How to Graph: Draw a straight line connecting $(6, 0)$ and $(0, 6)$. You can check another point, like $(3, 3)$, because $3+3=6$.

4) $y = \frac{1}{2}x - 5$

* Type: Slanted Line (Slope-Intercept Form).
* Y-intercept ($b$): $-5$. Start by plotting a point at $(0, -5)$ on the y-axis.
* Slope ($m$): $\frac{1}{2}$. This means "rise 1, run 2".
* How to Graph:
1. Plot the point $(0, -5)$.
2. From there, go up 1 unit and right 2 units to plot the next point at $(2, -4)$.
3. Go back to $(0, -5)$, go down 1 unit and left 2 units to plot a point at $(-2, -6)$.
4. Connect these points with a straight line.

5) $x = 4$

* Type: Vertical Line.
* Reasoning: The equation says that $x$ is always $4$, no matter what $y$ is.
* How to Graph: Find $4$ on the horizontal x-axis. Draw a straight vertical line up and down through that number. It passes through points like $(4, 0)$, $(4, 2)$, and $(4, -3)$.

6) $y = \frac{1}{4}x + 3y$

* Type: Slanted Line passing through the origin.
* Step 1: Simplify. We need to get $y$ by itself.
* Subtract $3y$ from both sides: $-2y = \frac{1}{4}x$
* Divide by $-2$: $y = -\frac{1}{8}x$
* Y-intercept: $0$. The line starts at the origin $(0,0)$.
* Slope: $-\frac{1}{8}$. This means "down 1, right 8" or "up 1, left 8".
* How to Graph:
1. Plot the point $(0, 0)$.
2. Since the grid only goes to $6$ on the right, we can't go right 8. Instead, go the opposite direction: Up 1 and Left 8. However, the grid only goes to $-6$ on the left.
3. Let's find a point that fits on the grid. If we choose $x = 4$, then $y = -\frac{1}{8}(4) = -0.5$. Point: $(4, -0.5)$.
4. If we choose $x = -4$, then $y = -\frac{1}{8}(-4) = 0.5$. Point: $(-4, 0.5)$.
5. Draw a line through $(0,0)$, $(4, -0.5)$, and $(-4, 0.5)$. It will be a very flat line going downwards from left to right.

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Final Answer:
1. Horizontal line crossing the y-axis at -4.
2. Line passing through (0, 3) and (1, 5).
3. Line connecting (6, 0) and (0, 6).
4. Line passing through (0, -5) and (2, -4).
5. Vertical line crossing the x-axis at 4.
6. Line passing through (0, 0), (4, -0.5), and (-4, 0.5).