use the slope intercept form to graph the equation y=2x+2
since this equation is already in the slope-intercept form, we can readily determine the slope and y-intercept.
note that in slope-intercept form , y = mx + b,
m is the slope ; and
b = y-intercept
thus in the given equation, y = 2x + 2
m = 2 ; and
b = 2
since y-intercept is a point on the line intersecting the y-axis, you plot on the Cartesian plane the point (0,2).
then we use the slope. since slope is rise/run and the slope we got is 2, the rise/run ratio = 2/1 , meaning, you go 2 points up and then 1 point to the right. the point you should get must be (1,4) -- because from (0,2), (0+1,2+2)=(1,4) . since two points determine a line, you can now plot the equation.
hope this helps~ :)
To graph the equation y = 2x + 2 using the slope-intercept form, you need to understand the components of the equation.
The slope-intercept form is in the format y = mx + b, where:
- "m" represents the slope of the line.
- "b" represents the y-intercept, which is the point where the line intersects the y-axis.
In the equation y = 2x + 2:
- The coefficient of "x" is 2, which is the slope of the line.
- The constant term is 2, which is the y-intercept.
To graph the equation, follow these steps:
1. Start by plotting the y-intercept on the graph. In this case, the y-intercept is the point (0, 2). This means that the line passes through (0, 2).
2. Since the slope is positive 2, it means that for every increase of 1 in x, y increases by 2 units. From the y-intercept, move 1 unit to the right along the x-axis and 2 units up along the y-axis to find the next point (1, 4). Connect these two points with a straight line.
3. Repeat step 2 to find additional points. For example, if you move 1 unit to the left along the x-axis from the y-intercept, you will reach the point (-1, 0). Connect these points as well.
4. Extend the line so that it covers the entire graph.
Once you have connected the points, you will have the graph of the equation y = 2x + 2.