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Answer:
- point-slope equation: y +1 = -3/4(x -4)
- slope-intercept equation: y = -3/4x +2
Step-by-step explanation:
(a) You can find the slope from the two given points:
y-intercept: (0, 2)
and (4, -1)
The slope formula tells you ...
m = (y2 -y1)/(x2 -x1)
m = (-1 -2)/(4 -0) = -3/4
The point-slope equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y +1 = -3/4(x -4) . . . . . line with slope -3/4 through point (4, -1)
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(b) Adding -1 and eliminating parentheses gives ...
y = -3/4x +3 -1
y = -3/4x +2 . . . . . . . slope-intercept equation
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Check
The constant in the slope-intercept equation is 2, the value that was given as the y-intercept—as it should be.
