One of the two equations listed in each problem matches the graph. Determine which equation is represented by the graph. Explain how you know your answer is correct
Y - 1 = 2(x + 1)
Or
6x + 3y = 9
To determine which equation matches the given graph, we can compare the slope and y-intercept values in each equation.
We can rewrite the first equation, Y - 1 = 2(x + 1), in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Simplifying the first equation, we have: Y - 1 = 2x + 2
Adding 1 to both sides, we have: Y = 2x + 3
Comparing this equation to the general form y = mx + b, we can see that the slope is 2 and the y-intercept is 3.
Now let's examine the second equation, 6x + 3y = 9.
To find the equation in slope-intercept form, we need to solve for y.
First, subtract 6x from both sides: 3y = -6x + 9
Next, divide both sides by 3: y = -2x + 3
Comparing this equation to y = mx + b, we see that the slope is -2 and the y-intercept is 3.
To determine which equation matches the given graph, we need to see if the slope and y-intercept values of either equation match the slope and y-intercept values of the graph.
If the graph has a slope of 2 and goes through the point (0,3), then the first equation, Y = 2x + 3, matches the graph.
If the graph has a slope of -2 and goes through the point (0,3), then the second equation, y = -2x + 3, matches the graph.
Since both equations have the same y-intercept of 3, we need to determine which equation has a slope of 2 or -2.
By examining the graph, if the line is going upwards from left to right (rising line), then the slope is positive (2 in this case). However, if the line is going downwards from left to right (falling line), then the slope is negative (-2 in this case).
Therefore, if the graph shows a rising line and goes through the point (0,3), then the equation represented by the graph is Y = 2x + 3.