Question

write an equation in point - slope form for the line that satisfies the given set of conditions. slope of 0, passes through (0, - 10)

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line and \((x_1,y_1)\) is a point on the line.

Step2: Identify the values of \(m\), \(x_1\) and \(y_1\)

We are given that the slope \(m = 0\) and the line passes through the point \((x_1,y_1)=(0,- 10)\).

Step3: Substitute the values into the point - slope formula

Substitute \(m = 0\), \(x_1 = 0\) and \(y_1=-10\) into the formula \(y - y_1=m(x - x_1)\).
We get \(y-(-10)=0\times(x - 0)\), which simplifies to \(y + 10=0(x - 0)\).

Answer:

\(y + 10 = 0(x - 0)\)