Respuesta :
Given:
[tex]\text{ line }y=-3x+6\text{ and point (1,-5).}[/tex]Aim:
We need to find the line which is parallel to y=-3x+6.
Explanation:
We know that the slope of the parallel lines is equal.
The given line is of the form
[tex]y=mx+b_1[/tex][tex]\text{where }m=-3\text{ and }b_1=6.[/tex]The slope of the required line is -3.
The slope-intercept form of the line equation for the required line is
[tex]y=mx+b[/tex]substitute m=-3, x=1, and y=-5 in the equation to find the value of b.
[tex]-5=-3(1)+b[/tex][tex]-5+3=b[/tex][tex]b=-2[/tex]Substitute m=-3 and b= -2 in the slope intercept line equation.
[tex]y=(-3)x+(-2)[/tex][tex]y=-3x-2[/tex]Final answer:
Teh slope-intercept equation is
[tex]y=-3x-2[/tex]