Graphing Linear Equations: Practice

Substitute each pair into $3x - 2y = 6$. For $(4, 3)$:

$3(4) - 2(3) = 12 - 6 = 6$

So $(4, 3)$ is a solution. The others give $0$, $-6$, and $1$.

The x-intercept is where the line meets the x-axis, so read where it crosses the horizontal axis.

$\text{The crossing sits at } x = 3, \; y = 0$

So the x-intercept is $(3, 0)$. The point $(0, 2)$ is the y-intercept, not the x-intercept.

Set $y = 0$ and solve for $x$.

$4x - 0 = 8, \qquad 4x = 8, \qquad x = 2$

So the x-intercept is $(2, 0)$.

The line is flat and every marked point sits at the same height, three units above the x-axis.

$\text{every point has } y = 3$

So the equation is $y = 3$. A horizontal line fixes $y$ and leaves $x$ free.

The y-axis is crossed at the y-intercept, the point whose x-coordinate is $0$.

$(0, 5) \;\Rightarrow\; x = 0$

So the line crosses the y-axis at $(0, 5)$. The point $(2, 0)$ is the x-intercept.

Every point on $x = -4$ has x-coordinate $-4$, whatever its y-coordinate.

$(-4,\, 1) \;\Rightarrow\; x = -4$

So $(-4, 1)$ is on the line. The others have x-coordinates $4$, $1$, and $0$.

Substitute each pair into $2x + 3y = 0$. For $(3, -2)$:

$2(3) + 3(-2) = 6 - 6 = 0$

So $(3, -2)$ is on the line. The others give $12$, $13$, and $5$.

Set $y = 0$ and solve for $x$.

$5x + 2(0) = 10, \qquad 5x = 10, \qquad x = 2$

So the x-intercept is $(2, 0)$.

By definition, an x-intercept is where the graph meets the x-axis, and every point on the x-axis has $y = 0$.

$\text{x-intercept} \;\Rightarrow\; y = 0$

That is why you set $y = 0$ to find it.

Set $x = 0$ and solve for $y$.

$0 - 3y = 9, \qquad -3y = 9, \qquad y = -3$

So the y-intercept is $(0, -3)$, below the x-axis.

At the x-intercept $y = 0$, so substitute and solve for $x$.

$x + 2(0) = 8, \qquad x = 8$

So $k = 8$ and the x-intercept is $(8, 0)$.

A point on the x-axis has $y = 0$, so it must be the x-intercept. Set $y = 0$ in $2x + 5y = 10$.

$2x = 10, \qquad x = 5$

So the point is $(5, 0)$. The others are not on the line or not on the x-axis.