Q. 102 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation of the y-axis.

Step-by-Step Solution

Answer

Equation of the y-axis: $x=0$

Step 1. Finding the equation of y-axis

Slope-intercept form of line: $y=mx+b$

Taking two points on y-axis: $(0,0), (0,d)$

Putting $(0,0)$we get, $0=m\left(0\right)+b$

$0=0+b$

$b=0$

Equation becomes, $y=mx$

$y=\frac{y_2-y_1}{x_2-x_1}\left(x\right)$

$y=\frac{d-0}{0-0}\left(x\right)$

$y=\frac{d}{0}\left(x\right)$

$x=\frac{\left(0\right)\left(y\right)}{d}$

$x=0$

Step 2: Write the equation in standard form

Rearrange and simplify the equation.

Step 3: Apply the solution method

Use factoring, quadratic formula, substitution, or other methods.

Step 4: Verify the solution(s)

Check solutions in the original equation.

Step 5: State the final answer

List all valid solutions.

Step 6: Conclude with the answer

Equation of the y-axis: $x=0$