To determine the equation of a horizontal line that contains the point $$(-1, 4)$$, apply the point-slope method.

**Step 1 — Identify the components:** The slope of any horizontal line is $$m = 0$$, and the specific point is $$(x_1, y_1) = (-1, 4)$$.

**Step 2 — Substitute into the point-slope form** $$y - y_1 = m(x - x_1)$$:
$$y - 4 = 0(x - (-1))$$

**Step 3 — Simplify:** Expanding and multiplying by zero yields:
$$y - 4 = 0$$
$$y = 4$$

The final equation of the line is $$y = 4$$.

Claude

To find the equation of a horizontal line containing the point $$(-2, -6)$$, substitute its given point and zero slope into the point-slope form.

**Step 1 — Identify the slope:** Every horizontal line has a slope of $$0$$, so $$m = 0$$.

**Step 2 — Identify the point:** The given point is $$(x_1, y_1) = (-2, -6)$$.

**Step 3 — Substitute into the point-slope form** $$y - y_1 = m(x - x_1)$$:
$$y - (-6) = 0(x - (-2))$$

**Step 4 — Simplify:** Distributing zero eliminates the entire right side of the equation:
$$y + 6 = 0$$
$$y = -6$$

**Step 5 — Write in slope-intercept form:** Although $$y = -6$$ is already in the $$y = b$$ format characteristic of a horizontal line, it could also be explicitly written as $$y = 0x - 6$$.

Finding the Equation of a Horizontal Line Through $$(-2, -6)$$ Using Point-Slope Form

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OpenStax Intermediate Algebra

To formulate the equation of a horizontal line passing through the point $$(-3, 8)$$, use the point-slope procedure.

**Step 1 — Identify the slope and point:** A horizontal line always has a slope of $$0$$, so $$m = 0$$. The given point is $$(x_1, y_1) = (-3, 8)$$.

**Step 2 — Substitute into the point-slope form** $$y - y_1 = m(x - x_1)$$:
$$y - 8 = 0(x - (-3))$$

**Step 3 — Simplify:** Multiplying the right side by zero eliminates the expression:
$$y - 8 = 0$$
$$y = 8$$

The final equation is $$y = 8$$, affirming that a horizontal line invariably takes the form $$y = b$$.

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