Answer:
y = 2x - 1
Step-by-step explanation:
To find out the equation of the line, you will always need the following information in order to determine the linear equation in slope-intercept form, y = mx + b:
1. 2 sets of ordered pairs (x, y)
2. Slope (m)
3. Y-intercept (b)
First, we need to choose 2 points from the graph to solve for the slope:
Let (x1, y1) = (0, -1)
(x2, y2) = (3, 5)
Substitute these values into the following slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{5 - (-1)}{3 - 0} = \frac{5 + 1}{3} = \frac{6}{3} = 2[/tex]
Therefore, the slope (m) = 2.
Next, we need the y-intercept, (b). The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The y-coordinate of the point (0, -1) is the y-intercept. Hence, the y-intercept (b) = -1.
Given our slope, m = 2, and the y-intercept (b) = -1, the linear equation is:
y = 2x - 1
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