The slope-intercept form is y = mx + b where:
m= slope
b = y-intercept (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.)
To start with, you’ll need two ordered pairs (x,y) from the line to solve for slope.
For the first graph:
Let (x1,y1) = (0,2)
(x2,y2) = (2,4)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = (4 - 2)/(2 - 0)
m = 2/2 = 1
Therefore, the slope (m) = 1.
Next, for the y-intercept, the point where it crosses the y-axis is at point (0, 2). Therefore, the y-intercept (b) = 2.
Thus, the linear equation of the first graph in slope-intercept form is: y = x + 2.
For the 2nd graph, do the same steps as we have done in the 1st graph:
Choose 2 ordered pairs:
Let (x1,y1) = (0,2) — right off the bat, this is the y-intercept.
(x2,y2) = (2,0)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = (0 - 2)/(2 - 0)
m = -2/2 = -1
Therefore, the slope (m) = 1.
For the y-intercept, I noted earlier that (0,2) is the y-intercept. Hence, b = 2.
The linear equation in slope-intercept form of the 2nd graph is: y = -x + 2
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