Find the slope for each equation.
$y=2 x+3$
Answer (1)
The equation is in the form y = m x + b , where m is the slope. The given equation is y = 2 x + 3 .
Comparing with the slope-intercept form, the slope is 2 .
Therefore, the slope of the equation is 2 .
Explanation
Identify the equation The given equation is y = 2 x + 3 . We need to find the slope of this equation.
Recall 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.
Compare the equation Comparing the given equation y = 2 x + 3 with the slope-intercept form y = m x + b , we can see that the coefficient of x is 2 .
Determine 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 of the line representing this relationship tells you how much the test score increases for each additional hour of studying. Similarly, in economics, the slope of a supply curve indicates how much the quantity supplied changes for each unit change in price. These concepts help in making informed decisions and predictions in various fields.
