Answer:
See long explanation & picture below.
Explanation:
See the picture below.
To graph do this:
y = x + 3
Start by graphing the y-intercept.
The y-intercept of y = mx + b is b, so here it is 3.
3 is a point on the y-axis, so its coordinates are (0, 3).
Now you use the slope to get other points.
The slope is m in y = mx + b.
In y = x + 3, it is as if you have y = 1x + 3, so the slope, m = 1.
The slope = 1
slope = rise/run
rise is up and down.
run is left and right
A slope of 1 is the same as a slope of 1/1.
That is a rise of 1 and a run of 1.
You start at the y-intercept, and your next point is 1 unit up and 1 unit to the right. See the other points in red up and to the right of (0, 3).
Then you draw a red line passing through all the red points and you extend it in both directions.
You have graphed the equation y = x + 3
To graph y = 4x - 6, use the same method.
The y-intercept is -6, so you plot a point on the y-axis at y = -6 in purple.
The slope is 4. 4 is the same as 4/1, so go 4 up and 1 right to get the next point. You can get a few points on the line this way.
Connect the purple points with a purple line and extend it in both directions.
You have now graphed y = 4x - 6
The intersection of the two lines is shown with a big green dot.
That is the solution of the system of equations.
The solution of the system of equations is the point of intersection of the two lines. You already knew it was (3, 6), and you were correct.