Questions: (a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope. (b) Write the equation using function notation where y=f(x). (2,-8) ; m=0

(a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope.
(b) Write the equation using function notation where y=f(x).
(2,-8) ; m=0

Transcript text: (a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope. (b) Write the equation using function notation where $y=f(x)$. \[ (2,-8) ; m=0 \] Part: $0 / 2$ Part 1 of 2

Solution

Solution Steps

Step 1: Identify the Given Information

We are given a point $(2, -8)$ and a slope $m = 0$. We need to find the equation of the line in slope-intercept form and function notation.

Step 2: Use the Slope-Intercept Form

The slope-intercept form of a line is given by the equation: \[ y = mx + b \] Substituting the given slope $m = 0$ and the point $(x_1, y_1) = (2, -8)$ into the equation, we solve for the y-intercept $b$: \[ -8 = 0 \cdot 2 + b \implies b = -8 \]

Step 3: Write the Equation in Slope-Intercept Form

Substitute the values of $m$ and $b$ into the slope-intercept form: \[ y = 0x - 8 \] This simplifies to: \[ y = -8 \]

Step 4: Write the Equation in Function Notation

In function notation, the equation is written as: \[ f(x) = 0x - 8 \] This simplifies to: \[ f(x) = -8 \]