Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3
To determine the graph that represents the system of equations y = 3x + 3 and y = –x – 3, we can start by graphing each equation individually and then analyze the intersection point.
Step 1: Graph the equation y = 3x + 3
To graph this linear equation, we'll start with the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Here, the slope (m) is 3, and the y-intercept (b) is 3.
Plot the y-intercept at (0, 3), and use the slope to find more points. For example, if we increase x by 1, y will increase by 3 since the slope is 3.
Now, let's plot those points and connect them with a straight line:
Step 2: Graph the equation y = -x - 3
This linear equation is already in slope-intercept form, where the slope (m) is -1, and the y-intercept (b) is -3.
Plot the y-intercept at (0, -3), and use the slope to find more points. For every increase of 1 in x, y will decrease by 1, as the slope is -1.
Plot those points and connect them with a straight line:
Step 3: Analyze the intersection point
Now we have graphed both equations, we can observe that the graphs intersect at (-2, -3). This intersection point represents the solution to the system of equations.
So, the graph that represents the system of equations y = 3x + 3 and y = -x - 3 is:
(Resource: graph is shown)
To determine which graph represents the given system of equations, we can start by noting the slopes and y-intercepts of the two equations.
The first equation, y = 3x + 3, has a slope of 3 and a y-intercept of 3. This means that for every increase of 1 in x, the corresponding y-value increases by 3. It also means that the line intersects the y-axis at the point (0, 3).
The second equation, y = -x - 3, has a slope of -1 and a y-intercept of -3. This means that for every increase of 1 in x, the corresponding y-value decreases by 1. It intersects the y-axis at the point (0, -3).
To plot these equations on a graph, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, since the slope is 3 and the y-intercept is 3, we can start at the point (0,3) and use the slope to find additional points on the line. From (0,3), we can move 1 unit to the right and 3 units up to plot another point. Connecting these points, we get a line that slopes upward.
For the second equation, with a slope of -1 and a y-intercept of -3, we start at the point (0,-3) and use the slope to find more points on the line. From (0,-3), we can move 1 unit to the right and 1 unit down to plot another point. Connecting these points gives a line that slopes downward.
In summary, the equations describe two lines: one with a positive slope (y = 3x + 3) and another with a negative slope (y = -x - 3). To identify the graph that represents these equations, look for the pair of lines on the graph with these characteristics.
In google type:
functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs
When page be open in blue recatacangle type:
3x+3
In grey rectacangle type:
-x-3
Then click option Draw