Question

Find the equation of the line parallel to y = x - 3 that also intersects the point (3,-2).
y = [?]x + [ ]

Answer 1

The equation of the line is $y=x-5$

Explanation:

Given that the equation of the line parallel to the line is $y=x-3$

Slope:

Since, the given equation is of the form $y=mx+b$

Comparing the equations, the slope of the equation is given by

$m=1$

Thus, the slope is $m=1$

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Thus, substituting the point (3,-2) and the slope $m=1$ in the formula, we get,

$y+2=1(x-3)$

Simplifying, we get,

$y+2=x-3$

     $y=x-5$

Hence, the equation of the line is $y=x-5$