Write an equation in slope-intercept form for the line with slope -4 and $y$-intercept 3.
Answer (1)
Identify the slope m = − 4 and y-intercept b = 3 .
Substitute the values into the slope-intercept form y = m x + b .
Obtain the equation y = − 4 x + 3 .
The equation of the line is y = − 4 x + 3 .
Explanation
Understanding the Problem We are given the slope and y -intercept of a line, and we need to write the equation of the line in slope-intercept form. The slope-intercept form of a linear equation is given by y = m x + b , where m represents the slope of the line and b represents the y -intercept.
Identifying Slope and y-intercept We are given that the slope of the line is -4, so m = − 4 . We are also given that the y -intercept is 3, so b = 3 .
Substituting Values Now, we substitute the values of m and b into the slope-intercept form equation y = m x + b . Substituting m = − 4 and b = 3 , we get y = − 4 x + 3 .
Final Equation Therefore, the equation of the line in slope-intercept form is y = − 4 x + 3 .
Examples
Imagine you're tracking the water level in a tank that's draining at a constant rate. If the tank starts with 3 gallons and drains 4 gallons every minute, the equation y = − 4 x + 3 models the amount of water left in the tank after x minutes. This equation helps you predict when the tank will be empty, which is a practical application of linear equations in everyday scenarios.
