Find the slope for each equation.
$y=2 x+3$
Answer (1)
The equation is in the form y = 2 x + 3 .
Recognize that the slope-intercept form of a linear equation is y = m x + b , where m is the slope.
Identify the coefficient of x as the slope: m = 2 .
The slope of the equation is 2 .
Explanation
Understanding the Equation The given equation is y = 2 x + 3 . We need to find the slope of this equation.
Recognizing Slope-Intercept Form The equation is in slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept.
Identifying the Slope Comparing the given equation y = 2 x + 3 with the general form y = m x + b , we can identify the coefficient of x as the slope. In this case, the coefficient of x is 2.
Stating the Slope Therefore, the slope of the equation y = 2 x + 3 is 2.
Examples
Understanding the slope of a line is crucial in many real-world applications. For example, if you are analyzing the relationship between the number of hours studied and the score on a test, the slope would represent the average increase in score for each additional hour of study. Similarly, in economics, the slope of a supply curve represents the change in quantity supplied for each unit change in price. Knowing the slope helps in making predictions and informed decisions.
