Question

Slope intercept form that passes through (-2,2) and perpendicular to y=1/2x-3

Answer 1

$▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

The equation of line that passes through (-2,2) and perpendicular to y=1/2x-3 is :

$y = - 2x - 2$

$\large \boxed{ \mathfrak{Explanation}}$

The equation of given line is :

• $y = \dfrac{1}{2} x - 3$

here, we can infer that slope of the given line is $\dfrac{1}{2}$ by comparing it with the general equation of line.

Let the slope of line perpendicular to it be m, now as we know if the lines are perpendicular then the product of their slopes will be equal to -1,

that is :

• $m \times \dfrac{1}{2} = - 1$

let's solve for m (slope of perpendicular line) ~

• $m = - 1 \times 2$

• $m = - 2$

now, let's find the equation of line perpendicular to y=1/2x-3 using the point - slope form, ( by using point (-2 , 2) and slope (-2))

• $\mathrm{y - y_1 = m(x - x_1)}$

• $y - 2 = - 2(x - ( - 2))$

• $y - 2 = - 2(x + 2)$

• $y - 2 = - 2x - 4$

• $y = - 2x - 4 + 2$

hence, the required equation is :

• $y = - 2x - 2$

$\mathrm{✌TeeNForeveR✌}$