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
\(y = 4x- 45\)
