Respuesta :
To determine the equation of a line given that you know its slope and a point you can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where
m represents the slope of the line
(x₁,y₁) represents the coordinates of the point crossed by the line
We know that the slope of the line is m=-4 and the coordinates of the point are x₁=8 and y₁=-10, replace these values in the point-slope form:
[tex]\begin{gathered} y-(-10)=-4(x-8) \\ y+10=-4(x-8) \end{gathered}[/tex]To write the equation in slope-intercept form, first, distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+10=-4\cdot x+(-4)(-8) \\ y+10=-4x+32 \end{gathered}[/tex]Next, pass 10 to the right side of the equation by applying the opposite operation "-10" to both sides of it:
[tex]\begin{gathered} y+10-10=-4x+32-10 \\ y=-4x+22 \end{gathered}[/tex]The equation of the line is y=-4x+22
