To graph the system, we first graph the equations y = 1/4x + 7 and y = -2x - 2 on the same coordinate plane:
1. The equation y = 1/4x + 7 is a linear equation with a y-intercept of 7 and a slope of 1/4. This means the line will rise 1 unit for every 4 units it moves to the right.
2. The equation y = -2x - 2 is a linear equation with a y-intercept of -2 and a slope of -2. This means the line will drop 2 units for every 1 unit it moves to the right.
Now we will plot these lines on the coordinate plane:
y = 1/4x + 7 (blue line):
- Start by plotting the y-intercept at (0, 7).
- Use the slope of 1/4 to find another point on the line. Move up 1 unit and to the right 4 units to find another point.
- Draw a straight line through the two points to represent the equation y = 1/4x + 7.
y = -2x - 2 (red line):
- Start by plotting the y-intercept at (0, -2).
- Use the slope of -2 to find another point on the line. Move down 2 units and to the right 1 unit to find another point.
- Draw a straight line through the two points to represent the equation y = -2x - 2.
The graph will show two lines intersecting at a single point. This point represents the solution to the system of equations. By reading the coordinates of the intersection point from the graph, we can find the solution to the system of equations.
(Answer depends on the specific intersection point found on the graph.)
Solve the following system of linear equations by first graphing the system.
y=1/4x+7
y=−2x−2
(1 point)
1 answer