The equations of the graphed line and function can be written as:
f(x) = 1/2x + 2
y - 3 = 1/2(x - 2)
y - 1 = 0.5(x + 2)
<h3>What is the Equation of a Graphed Line?</h3>Equation of a graphed line can be expressed in:
Slope-intercept form as y = mx + b, where m = slope, b = y-intercept; or
Point-slope form as y - b = m(x - a), where (a, b) is a point and m = slope.
Find the slope (m) of the line:
Slope (m) = change in y / change in x = 1/2 = 0.5
y-intercept (b) = 2
To express the graphed line in slope-intercept form, substitute m = 1/2 and b = 2 into f(x) = mx + b:
f(x) = 1/2x + 2.
Using the point-slope form, write the equation by substituting m = 1/2 and (a, b) = (2, 3) into y - b = m(x - a):
y - 3 = 1/2(x - 2)
Or substitute m = 0.5 and (a, b) = (-2, 1) into y - b = m(x - a):
y - 1 = 0.5(x - (-2))
y - 1 = 0.5(x + 2)
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