Question

square grids
$y = \frac{1}{4}x - 1$
$y = -x + 2$
$y = x + 1$
$y = 4/2 x + 4$
$y = -3x - 3$
$y = 1$

Explanation:

Step1: Identify slope-intercept form

All equations use $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

Step2: Plot $y=\frac{1}{4}x-1$

• Y-intercept: $(0, -1)$
• Slope: $\frac{1}{4}$, so from $(0,-1)$, move 4 right, 1 up to $(4,0)$. Draw line through points.

Step3: Plot $y=-x+3$

• Y-intercept: $(0, 3)$
• Slope: $-1$, so from $(0,3)$, move 1 right, 1 down to $(1,2)$. Draw line through points.

Step4: Plot $y=x+1$

• Y-intercept: $(0, 1)$
• Slope: $1$, so from $(0,1)$, move 1 right, 1 up to $(1,2)$. Draw line through points.

Step5: Plot $y=\frac{4}{3}x-4$

• Y-intercept: $(0, -4)$
• Slope: $\frac{4}{3}$, so from $(0,-4)$, move 3 right, 4 up to $(3,0)$. Draw line through points.

Step6: Plot $y=-3x-3$

• Y-intercept: $(0, -3)$
• Slope: $-3$, so from $(0,-3)$, move 1 right, 3 down to $(1,-6)$ or 1 left, 3 up to $(-1,0)$. Draw line through points.

Step7: Plot $y=11$

• Horizontal line at $y=11$, passing through all points where $y=11$ (e.g., $(0,11), (5,11)$).

Answer:

Each line is plotted as follows:

1. $y=\frac{1}{4}x-1$: Line through $(0,-1)$ and $(4,0)$
2. $y=-x+3$: Line through $(0,3)$ and $(1,2)$
3. $y=x+1$: Line through $(0,1)$ and $(1,2)$
4. $y=\frac{4}{3}x-4$: Line through $(0,-4)$ and $(3,0)$
5. $y=-3x-3$: Line through $(0,-3)$ and $(-1,0)$
6. $y=11$: Horizontal line at $y=11$ across the grid