Question

a line passes through (9, –9) and (10, –5).write an equation for the line in point-slope form. rewrite the equation in standard form using integers. y 9 = (x – 9); –4x y = –45 y 9 = (x 9); –4x y = –45 y – 9 = (x 9); –4x y = 45 y – 9 = (x – 9); –4x y = 45

Answer 1

The equation of the line in point-slope form is given by:
 $y-yo = m (x-xo)$
 Where,
 (xo, yo): point that belongs to the line
 m: slope of the line
 The slope is given by:
 $m = \frac{y2-y1}{x2-x1}$
 Substituting values:
 $m = \frac{-5-(-9)}{10-9}$
 Rewriting:
 $m = \frac{-5+9}{10-9}$
 $m = \frac{4}{1}$
 $m=4$
 Now we choose an ordered pair:
 $(xo, yo) = (10, -5)$
 Substituting values we have:
 $y-(-5)=4(x-10)$
 $y+5=4(x-10)$
 We now rewrite the equation in its standard form:
 $y = mx + b$
 Where,
 b: cut with the y axis.
 We have then:
 $y = 4x - 40 - 5 y = 4x - 45$
 Answer:
 point-slope form:
 $y+5=4(x-10)$
 or
 $y+9=4(x-9)$
 standard form
 $y = 4x- 45$