In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Intersecting the -axis at a distance of 3 units to the left of origin with slope .
The line intersects the x-axis at a distance of 3 units to the left of origin, so the point of intersection is (-3, 0).
Given slope m = -2 and point (x₀, y₀) = (-3, 0), using the point-slope form:
y - y₀ = m(x - x₀)
Substituting the values:
y - 0 = -2(x - (-3))
y = -2(x + 3)
y = -2x - 6
Therefore, the equation of the line is y = -2x - 6 or 2x + y + 6 = 0.
Explanation
The question requires finding the equation of a line using the point-slope form. The line passes through (-3, 0) on the x-axis (3 units left of origin means x = -3) and has slope -2. Using the point-slope formula y - y₀ = m(x - x₀) from the textbook, we substitute the given values to derive the equation.
Solution Steps
Step 1: Identify the point on x-axis: 3 units left of origin = (-3, 0)
Step 2: Apply point-slope form: y - y₀ = m(x - x₀)
Step 3: Substitute values: y - 0 = -2(x - (-3))
Step 4: Simplify: y = -2(x + 3) = -2x - 6
Step 5: Final equation: y = -2x - 6 or 2x + y + 6 = 0