2x+y=5
slope-intercept form is y=mx + b
so if you put that in this form it would be:
y= -2x + 5
To solve the equation 2x + y = 5, we need to find the values of x and y that satisfy the equation. This equation is a linear equation in two variables, x and y.
There are several methods to solve this equation, but let's use the method of substitution:
1. Solve one of the equations for one variable in terms of the other. Here, we can solve the equation for y:
y = 5 - 2x
2. Substitute the expression for y in terms of x into the other equation. Replace y with 5 - 2x in the equation 2x + y = 5:
2x + (5 - 2x) = 5
3. Simplify the equation by combining like terms:
2x + 5 - 2x = 5
5 = 5
4. In this case, we obtained a true equation 5 = 5. This means that any value of x and y will satisfy the equation. Therefore, the solution is infinite, and the equation represents a line.
To graph this equation, we can rewrite it in the form of y = mx + c, where m is the slope and c is the y-intercept:
2x + y = 5
y = -2x + 5
This equation has a slope of -2 and a y-intercept of 5. To plot the graph, you can choose any values for x and find the corresponding y values. Connect the points to obtain a straight line.