Questions: Characteristics of Linear Functions For each function below, identify the Slope, horizontal-intercept and vertical-intercept Write your numerical answers as whole numbers or reduced fractions. Write your intercepts as ordered pairs. If a slope or intercept Does Not Exist, write DNE

$Characteristics of Linear Functions For each function below, identify the Slope, horizontal-intercept and vertical-intercept Write your numerical answers as whole numbers or reduced fractions. Write your intercepts as ordered pairs. If a slope or intercept Does Not Exist, write DNE$

Transcript text: Characteristics of Linear Functions For each function below, identify the Slope, horizontal-intercept and vertical-intercept Write your numerical answers as whole numbers or reduced fractions. Write your intercepts as ordered pairs. If a slope or intercept Does Not Exist, write DNE

Solution

Solution Steps

Solution Approach

To identify the slope, horizontal-intercept, and vertical-intercept of a linear function, we need to:

Identify the slope (m) from the linear equation in the form y = mx + b.
Determine the vertical-intercept (0, b) from the same equation.
Find the horizontal-intercept by setting y to 0 and solving for x.

Step 1: Identify the Slope

The slope $ m $ of the linear function given by the equation $ y = 2x + 3 $ is $ 2.0 $.

Step 2: Determine the Vertical-Intercept

The vertical-intercept occurs when $ x = 0 $. From the equation, substituting $ x = 0 $ gives: \[ y = 2(0) + 3 = 3.0 \] Thus, the vertical-intercept is $ (0, 3.0) $.

Step 3: Calculate the Horizontal-Intercept

The horizontal-intercept occurs when $ y = 0 $. Setting $ y = 0 $ in the equation: \[ 0 = 2x + 3 \] Solving for $ x $: \[ 2x = -3 \implies x = -\frac{3}{2} = -1.5 \] Thus, the horizontal-intercept is $ (-1.5, 0) $.