Graphing linear equations using a table of values worksheet with four practice problems.

To solve this problem, we need to find three points $(x, y)$ that lie on each line shown in the graphs. We do this by looking at the grid and finding where the lines cross the intersections of the grid lines (the "crosshairs").

Here is the step-by-step breakdown for each problem:

Problem 1)

Line A: This is a vertical line. Notice that no matter how high or low you go, the x-value stays the same. It crosses the x-axis at $-5$.
* Point 1: $x = -5$, pick any $y$ (e.g., $0$) $\rightarrow (-5, 0)$
* Point 2: $x = -5$, pick another $y$ (e.g., $3$) $\rightarrow (-5, 3)$
* Point 3: $x = -5$, pick another $y$ (e.g., $-3$) $\rightarrow (-5, -3)$

Line B: This is a diagonal line going down. Let's find clear intersections.
* It crosses the y-axis at $4$. So, one point is $(0, 4)$.
* Moving right 2 units and down 1 unit, it hits $(2, 3)$.
* Moving right another 2 units and down 1 unit, it hits $(4, 2)$.
* Another easy one is where it crosses the x-axis? No, it doesn't cross cleanly there. Let's check left. Left 2, up 1 from $(0,4)$ is $(-2, 5)$.
* Let's use: $(0, 4), (2, 3), (4, 2)$.

Problem 2)

Line A: This line goes down steeply.
* It crosses the y-axis at $4$. Point: $(0, 4)$.
* It crosses the x-axis at $3$. Point: $(3, 0)$.
* Let's check another point. If we go left 1 from $(0,4)$, we go up roughly 1.3? No, let's look closer. From $(3,0)$ to $(0,4)$, the rise is $4$ and run is $-3$. Slope is $-4/3$.
* Let's try integer coordinates.
* At $x = -3$, $y = 8$? (Off chart mostly).
* Let's re-examine the graph. Line A passes through $(0, 4)$ and looks like it passes through $(3, 0)$. Let's check $(-3, 8)$... wait, looking at the grid, at $x=-3$, line A is at $y=8$? The grid only goes to $6$.
* Let's look for another clear point. At $x = 1.5$, $y=2$? Hard to read.
* Let's look at Line A again. It passes through $(0,4)$. Does it pass through $(1, 2.6)$? No.
* Let's look at the other intersection. It seems to pass through $(-1.5, 6)$?
* Actually, let's look at Line B first, it might be easier.
* Line B: Passes through $(0, -2)$ and $(2, 0)$. Slope is $1$.
* Point 1: $(0, -2)$
* Point 2: $(2, 0)$
* Point 3: $(-2, -4)$ or $(4, 2)$. Let's use $(4, 2)$.
* Back to Line A: It passes through $(0, 4)$ and $(3, 0)$.
* Point 1: $(0, 4)$
* Point 2: $(3, 0)$
* To find a third integer point, we follow the pattern: Down 4, Right 3. Or Up 4, Left 3.
* From $(0,4)$, go Left 3, Up 4 $\rightarrow (-3, 8)$. This is off the visible grid but valid.
* Is there a simpler point? Maybe the slope is different? Let's check $(-1, 5.something)$.
* Let's assume the standard integer points visible or easily extrapolated: $(0, 4), (3, 0), (-3, 8)$.

Problem 3)

Line A: This line goes up slowly.
* It crosses the y-axis at $1$. Point: $(0, 1)$.
* It crosses the x-axis at $-4$? No, at $x=-4$, $y=0$. Yes. Point: $(-4, 0)$.
* Let's check the slope. Rise 1, Run 4.
* Next point: From $(0,1)$, go Right 4, Up 1 $\rightarrow (4, 2)$.
* Points: $(-4, 0), (0, 1), (4, 2)$.

Line B: This is a horizontal line.
* It stays at $y = -2$ forever.
* Point 1: $(0, -2)$
* Point 2: $(2, -2)$
* Point 3: $(-4, -2)$

Problem 4)

Line A: This line goes down.
* It crosses the y-axis at $3$. Point: $(0, 3)$.
* It crosses the x-axis at $6$. Point: $(6, 1)$? No, at $x=6$, $y=1$. Let's check slope.
* From $(0,3)$ to $(6,1)$: Down 2, Right 6. Slope $-1/3$.
* Let's check intermediate points.
* $x=3$, $y=2$. Point: $(3, 2)$.
* $x=-3$, $y=4$. Point: $(-3, 4)$.
* Points: $(0, 3), (3, 2), (6, 1)$.

Line B: This line goes up steeply.
* It crosses the x-axis at $-2$. Point: $(-2, 0)$.
* It crosses the y-axis at $-2$? No, looks like $(0, -2)$ is on Line B? Wait, Line B passes through $(-2, 0)$ and $(0, -2)$? That would mean slope is $-1$. But Line B is going UP from left to right.
* Let's re-read Graph 4 carefully.
* Line B starts bottom-left and goes top-right.
* It passes through $(-2, -2)$? No.
* It passes through $(-1, -1)$?
* It passes through $(0, -1)$? No.
* Let's look at the intercepts.
* X-intercept: $(-2, 0)$.
* Y-intercept: Looks like $(0, 2)$? No, that's too high.
* Let's trace from $(-2, 0)$. If I go right 1, up 1, I hit $(-1, 1)$. Then $(0, 2)$. Then $(1, 3)$.
* Let's check the graph again. Line B passes through $(-2, 0)$ and $(0, 2)$?
* Looking at the arrow for B, it passes through $(-3, -1)$, $(-2, 0)$, $(-1, 1)$, $(0, 2)$.
* Yes, the slope is $1$.
* Points: $(-2, 0), (0, 2), (2, 4)$.

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Final Answer

1)
Line A)
$x$: $-5$, $-5$, $-5$
$y$: $0$, $3$, $-3$
*(Note: Any y-values are correct as long as x is -5)*

Line B)
$x$: $0$, $2$, $4$
$y$: $4$, $3$, $2$

2)
Line A)
$x$: $0$, $3$, $-3$
$y$: $4$, $0$, $8$

Line B)
$x$: $0$, $2$, $4$
$y$: $-2$, $0$, $2$

3)
Line A)
$x$: $-4$, $0$, $4$
$y$: $0$, $1$, $2$

Line B)
$x$: $0$, $2$, $-4$
$y$: $-2$, $-2$, $-2$
*(Note: Any x-values are correct as long as y is -2)*

4)
Line A)
$x$: $0$, $3$, $6$
$y$: $3$, $2$, $1$

Line B)
$x$: $-2$, $0$, $2$
$y$: $0$, $2$, $4$