Question

Write an equation in standard form of the horizontal line and the vertical line that pass through the point. $$(10,-3)$$

Short answer

The standard form for the horizontal line passing through the point (10,-3) is \(y=-3\) and for the vertical line it's \(x=10\).

Step-by-step solution

Equation for Horizontal Line

Start with the general form of a horizontal line, which is \(y=a\). Replace the \(a\) with the y-value of the given point. For the provided point (10, -3), the y-value is -3. Therefore, the horizontal line that passes through this point will have the equation \(y=-3\).

Equation for Vertical Line

Now, let's ascertain the equation of the vertical line that passes through the provided point. A vertical line follows the equation \(x=b\). Here, \(b\) should be replaced by the x-value of the point, which in this case is 10. Consequently, the vertical line passing through the point has the equation \(x=10\).