9514 1404 393
Answer:
linear equation in the point-slope form
Explanation:
There are many forms an equation for a line may take. Some of the ones commonly seen are ...
ax +by = c . . . . standard form (a,b,c mutually prime integers; a>0)
y = mx + b . . . . slope-intercept form (m=slope; b=y-intercept)
y -k = m(x -h) . . . . point-slope form (m=slope, (h, k)=point)
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and some additional ones I commonly use are ...
x/(x-intercept) +y/(y-intercept) = 1
y = m(x -h) +k . . . . variation of point-slope form (m=slope; (h, k)=point)
y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . two-point form (points (x1, y1) and (x2, y2))
bx -ay = bh-ak . . . . line perpendicular to standard form line ax +by = c through point (h, k)
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If you compare these forms to the equation you're given, you see it matches the "point-slope form" for point (4, 2) and slope 7.