Question

The slope-intercept form of the equation of a line that passes through point $(–2,–13)$ is $y=5x–3$. What is the point-slope form of the equation for this line?

• A. $y–13=5(x–2)$
• B. $y+13=5(x+2)$
• C. $y–2=5(x–13)$
• D. $y+2=5(x+13)$

Answer 1

The correct option is B

$y+13=5(x+2)$

Explanation for the correct option:

The general equation of line in slope-intercept form is $y=mx+c$, where $m$ is the slope and $y$ intercept is $(0,c)$.

Compare the equation $y=5x–3$ with the equation $y=mx+c$, the value of slope $m$ is obtained as $5$.

The general equation of line in point-slope form is $y-q=m(x-p)$, where $m$ is the slope and $(p,q)$ is the point on the line.

Substitute $5$ for $m$, $–2$ for $p$, and $-13$ for $q$ in the equation $y-q=m(x-p)$ to obtain the required equation.

$y-(-13)=5(x-(-2\left)\right)$

$\therefore$ $y+13=5(x+2)$

Thus, the required equation is $y+13=5(x+2)$.

Hence, option (B) is the correct option.