equation $y=2 x+4 $?
Answer (1)
The equation y = 2 x + 4 is a linear equation in slope-intercept form.
The slope of the line is 2, and the y-intercept is 4.
The graph is a straight line that increases from left to right.
The equation represents a linear relationship between x and y , where y increases by 2 for every unit increase in x , and the line intersects the y-axis at 4. y = 2 x + 4
Explanation
Identify the Equation The given equation is y = 2 x + 4 . We need to analyze this equation.
Recognize Slope-Intercept Form The equation y = 2 x + 4 is in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept.
Determine Slope and Y-intercept In the equation y = 2 x + 4 , we can identify the slope m as 2 and the y-intercept b as 4. This means that for every increase of 1 in x , y increases by 2. The line crosses the y-axis at the point (0, 4).
Describe the Graph The graph of the equation y = 2 x + 4 is a straight line. It has a positive slope, so it increases from left to right.
Examples
Understanding linear equations like y = 2 x + 4 is crucial in many real-world scenarios. For instance, imagine a taxi service charges a fixed fee of $4 plus 2 p er mi l e . T h ee q u a t i o n y = 2x + 4 m o d e l s t hi ss i t u a t i o n , w h ere y i s t h e t o t a l cos t an d x$ is the number of miles traveled. By understanding the slope and y-intercept, you can easily calculate the cost for any distance or determine how far you can travel with a specific budget. This applies to budgeting, understanding rates, and making informed financial decisions.
