Graph the line.
$2 x+y=-4$
Answer (1)
Rewrite the equation in slope-intercept form: y = − 2 x − 4 .
Identify the y-intercept: ( 0 , − 4 ) .
Find the x-intercept by setting y = 0 : x = − 2 , so the x-intercept is ( − 2 , 0 ) .
Plot the points ( − 2 , 0 ) and ( 0 , − 4 ) and draw a line through them. The equation of the line is 2 x + y = − 4 .
Explanation
Understanding the Problem We are given the equation of a line: 2 x + y = − 4 . Our goal is to graph this line. To do this, we will first rewrite the equation in slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept. Then, we will find the x-intercept and plot both intercepts on the coordinate plane. Finally, we will draw a straight line through these two points.
Rewriting the Equation First, let's rewrite the given equation in slope-intercept form. We have 2 x + y = − 4 . Subtracting 2 x from both sides, we get y = − 2 x − 4 . From this equation, we can see that the slope m = − 2 and the y-intercept b = − 4 . This means the line crosses the y-axis at the point ( 0 , − 4 ) .
Finding the X-Intercept Next, let's find the x-intercept. To do this, we set y = 0 in the equation 2 x + y = − 4 and solve for x . So, we have 2 x + 0 = − 4 . Dividing both sides by 2, we get x = − 2 . This means the line crosses the x-axis at the point ( − 2 , 0 ) .
Plotting the Points and Drawing the Line Now we have two points on the line: the y-intercept ( 0 , − 4 ) and the x-intercept ( − 2 , 0 ) . We can plot these points on the coordinate plane and draw a straight line through them.
Final Answer The line passes through the points ( − 2 , 0 ) and ( 0 , − 4 ) . The equation of the line is y = − 2 x − 4 or 2 x + y = − 4 .
Examples
Lines are fundamental in many real-world applications. For example, in physics, the relationship between distance and time for an object moving at a constant speed can be represented by a line. In economics, supply and demand curves are often represented as lines. Understanding how to graph and analyze lines is crucial in these fields.
