Answer:
- y +4 = -7/8(x -7)
- y = -7/8x +17/8
Explanation:
Given two points, the equation for the line can be found by starting with determining the slope. Then the point-slope form can be used to find the equation. That form can be rearranged to give the slope-intercept form (or any other form you may desire.)
The slope formula is ...
m = (y2 -y1)/(x2 -x1)
m = (3 -(-4))/(-1 -7) = 7/-8 = -7/8
Then the point-slope form using the first point is ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y +4 = -7/8(x -7) . . . . . line with slope -7/8 through (7, -4)
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Eliminating parentheses, and subtracting 4 gives the slope-intercept equation:
y +4 = -7/8x +49/8 . . . eliminate parentheses
y = -7/8x +17/8 . . . . . subtract 4; slope-intercept equation
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The attached graph shows both forms of the equation draw the same line.