Question

what is an equation of the line that passes through the point (-5, -3) and is perpendicular to the line x + y = 2?

Explanation:

Step1: Find the slope of the given line

Rewrite $x + y=2$ in slope - intercept form $y=-x + 2$. The slope of this line is $m_1=-1$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of the required line be $m_2$. Then $m_1\times m_2=-1$. Since $m_1 = - 1$, we have $(-1)\times m_2=-1$, so $m_2 = 1$.

Step3: Use the point - slope form to find the equation of the line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-5,-3)$ and $m = 1$. Substitute these values: $y-(-3)=1\times(x - (-5))$.

Step4: Simplify the equation

$y + 3=x + 5$, which simplifies to $y=x+2$.

Answer:

$y=x + 2$