contestada

Let line $l_1$ be the graph of $3x + 4y = -14$. Line $l_2$ is perpendicular to line $l_1$ and passes through the point $(-5,7)$. If line $l_2$ is the graph of the equation $y=mx +b$, then find $m+b$.

Respuesta :

LammettHash

[tex]3x+4y=-14\implies y=-\dfrac{3x+14}4[/tex]

and so [tex]\ell_1[/tex] has slope -3/4. Then any line perpendicular to [tex]\ell_1[/tex] has slope 4/3.

Given that [tex]\ell_2\perp\ell_1[/tex] and [tex]\ell_2[/tex] passes through (-5, 7), its equation is

[tex]y-7=\dfrac43(x+5)\implies y=\dfrac{4x}3+\dfrac{41}3[/tex]

so that [tex]m=\frac43[/tex] and [tex]b=\frac{41}3[/tex], which gives

[tex]m+b=\dfrac{45}3=\boxed{15}[/tex]

Otras preguntas