9514 1404 393
Answer:
a) 3
b) 1
c) y = 3x +1
Step-by-step explanation:
Given:
A(1, 4), B(2, 7)
m = (y2 -y1)/(x2 -x1)
Find:
a) the slope of the line through these points
b) the y-intercept of the line through these points
c) the equation of the line through these points
Solution:
a) Using the given formula, the slope is ...
m = (7 -4)/(2 -1) = 3/1 = 3 . . . the slope of the line
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b) The y-intercept can be found from* ...
b = y1 -m·x1
b = 4 -3·1 = 1 . . . the y-intercept
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c) The equation in slope-intercept form is ...
y = mx +b
y = 3x +1
_____
* This equation for the y-intercept is not one you see often. It can be derived from the point-slope form of the equation of a line:
y -y1 = m(x -x1)
y = mx -m·x1 + y1 = mx +b . . . . eliminate parentheses, add y1
b = y1 -m·x1 . . . . . . . . solve for b
