Answer: To determine which equation gives the line shown on the graph, we need to examine the slope (m) and y-intercept (b) of the line.
Looking at the given options, we can determine the equation by comparing the slope and y-intercept values with the line on the graph.
The line on the graph passes through the point (0, 1) and (6, 13). We can calculate the slope using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the points (0, 1) and (6, 13):
m = (13 - 1) / (6 - 0)
m = 12 / 6
m = 2
Now, let's compare the slope and y-intercept values with the given equation options:
y = 2x - 4
y = x + 4
y = 2x + 4
y = -x - 4
From the calculation above, we determined that the slope of the line on the graph is 2. Comparing this with the slope values in the equation options, we find that options 1 and 3 have a matching slope of 2.
Next, we can compare the y-intercept of the line on the graph, which is (0, 1), with the y-intercept values in the equation options:
y = 2x - 4 -> y-intercept: -4
y = x + 4 -> y-intercept: 4
y = 2x + 4 -> y-intercept: 4
y = -x - 4 -> y-intercept: -4
From the comparison, we see that option 3, y = 2x + 4, matches both the slope and y-intercept of the line on the graph.
Therefore, the equation that gives the line shown on the graph is y = 2x + 4.
Explanation: