Graph this equation: [tex]y=2 x+5[/tex]
Answer (1)
Identify the equation as a linear equation in slope-intercept form: y = 2 x + 5 .
Determine the slope m = 2 and the y-intercept b = 5 .
Plot the y-intercept at (0, 5) and use the slope to find another point, such as (1, 7).
Draw a straight line through the points (0, 5) and (1, 7) to graph the equation y = 2 x + 5 .
Explanation
Understanding the Equation We are asked to graph the equation y = 2 x + 5 . This is a linear equation in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept.
Identifying Slope and Y-intercept In the given equation, y = 2 x + 5 , we can identify the slope m as 2 and the y-intercept b as 5. This means the line crosses the y-axis at the point (0, 5).
Finding Another Point To graph the line, we need at least two points. We already have one point, the y-intercept (0, 5). We can find another point using the slope. The slope of 2 can be written as 1 2 , which means for every 1 unit we move to the right on the x-axis, we move 2 units up on the y-axis.
Calculating the Second Point Starting from the y-intercept (0, 5), we move 1 unit to the right and 2 units up to find the next point. This gives us the point (1, 7).
Drawing the Line Now that we have two points, (0, 5) and (1, 7), we can draw a straight line through these points. This line represents the graph of the equation y = 2 x + 5 .
Final Answer The graph of the equation y = 2 x + 5 is a straight line that passes through the points (0, 5) and (1, 7). The line extends infinitely in both directions.
Examples
Understanding linear equations like y = 2 x + 5 is crucial in many real-world scenarios. For example, imagine you are saving money. If you start with $5 and save 2 e v ery w ee k , t h ee q u a t i o n y = 2x + 5 m o d e l syo u r t o t a l s a v in g s y a f t er x$ weeks. Graphing this helps visualize how your savings grow over time, showing the direct relationship between time and money saved.
