Math

QuestionIdentify the graph for the equation y=2x+2y=2x+2.

Studdy Solution

STEP 1

Assumptions1. The equation is in the form of y = mx + c, which is the slope-intercept form of a linear equation. . 'm' represents the slope of the line.
3. 'c' represents the y-intercept of the line.

STEP 2

Identify the slope and the y-intercept from the given equation.
The given equation is y=2x+2y =2x +2Here, 'm' (the slope) is2 and 'c' (the y-intercept) is2.

STEP 3

Understand the meaning of slope and y-intercept.
The slope of a line is the measure of the steepness of the line. A positive slope means the line rises as it moves to the right, while a negative slope means the line falls as it moves to the right.
The y-intercept is the point where the line crosses the y-axis. In this case, it is2, which means the line crosses the y-axis at the point (0,2).

STEP 4

To graph the equation, start by plotting the y-intercept. In this case, plot a point at (0,2) on the y-axis.

STEP 5

Next, use the slope to find another point on the line. The slope is2, which means for every1 unit increase in 'x', 'y' increases by2 units. So, from the y-intercept (0,2), move1 unit to the right and2 units up. This gives the point (1,4).

STEP 6

Plot the point (1,4) on the graph.

STEP 7

Draw a straight line through the points (0,2) and (1,4). This line represents the equation y=2x+2y =2x +2.
The graph that represents the equation y=2x+2y =2x +2 is a straight line that passes through the points (0,2) and (1,4), rising to the right.

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