Answer:
y = 4x - 3
Step-by-step explanation:
When writing an equation of a line, keep in mind that you 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, -3)
(x2, y2) = (1, 1)
Use the following slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Substitute the values of the coordinates into the formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - (-3)}{1 - 0} = \frac{1 + 3}{1} = \frac{4}{1} = 4[/tex]
Therefore, the slope (m) of the line = 4.
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, -3) is the y-intercept. Hence, the y-intercept (b) = -3.
Given our slope, m = 4, and the y-intercept (b) = -3, the linear equation is:
y = 4x - 3
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