Problem 44 - Algebra 1: Concepts and Skills

Question

Graph the function. $$ h(x)=x+5 $$

Step-by-Step Solution

Answer

The graph of the function \( h(x) = x+5 \) is a straight line with a slope of 1 and cuts the y-axis at \( y = 5 \).

Step 1: Understand the Function

This function \(h(x) = x + 5\) is in the form of a simple linear equation, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In our case, \(m = 1\) and \(b = 5\). The slope being 1 means for each step increase in \(x\), \(h(x)\) increases by 1. The y-intercept being 5 means when \(x = 0\), \(h(x)\) will be equal to 5.

Step 2: Draw the Y-intercept

Begin the graph by marking the y-intercept. In this case,when \(x = 0\), \(h(x) = 0 + 5 = 5\). So we make a point at \(y = 5\) on the y-axis.

Step 3: Use Slope to Draw the Line

Since the slope \(m = 1\), that means for each step increase in \(x\), \(h(x)\) increases by 1. From the y-intercept, move to the right one unit (as this is a step increase in \(x\)) and up one unit (as this is the corresponding increase in \(h(x)\)). Draw the line that passes through these points.