In writing an equation of a line, keep in mind that you ALWAYS need the following information in order to establish a linear equation:
1. 2 ordered pairs (x,y) on the line
2. Slope
We’ll use the following points:
(x1, y1) = (0, 9) ← y-intercept
(x2, y2) = (3, 3)
Substitute these values into the Slope formula:
m = (y2 - y1)/(x2 - x1)
m = (3 - 9)/(3 - 0)
m = -6/3
m = -2/1 or -2
The slope of the line is -2.
Next, we need to determine the y-intercept. The y-intercept is the y-coordinate of the point (0, b) where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.
In reference to your given graph, the line crosses the y-axis at point, (0, 9). These coordinates represent the y-intercept. Its y-coordinate, 9, is the value for “b” in slope-intercept form, y = mx + b.
Therefore, the linear equation in slope-intercept form is: y = -2x + 9.
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