Answer:
The line [tex]y = -3\, x + 6[/tex] goes through the point [tex](1,\, 3)[/tex] and has a slope of [tex](-3)[/tex].
Step-by-step explanation:
If the slope of a line is [tex]m[/tex] and the [tex]y[/tex]-intercept of that line is [tex]b[/tex] ([tex]m\![/tex] and [tex]b\![/tex] are constants), then [tex]y = m\, x + b[/tex] would be the slope-intercept equation of that line.
The slope of the line in this question is [tex]m = -3[/tex]. However, [tex]b[/tex], the [tex]y[/tex]-intercept of this line, still needs to be found. The equation of this line would be [tex]y = -3\, x + b[/tex] for some constant [tex]b\![/tex].
Since this line goes through [tex](1,\, 3)[/tex], [tex]x = 1[/tex] and [tex]y = 3[/tex] should satisfy the equation of this line. In other words, if [tex]x = 1\![/tex] and [tex]y = 3\![/tex] are substituted into [tex]y = -3\, x + b[/tex], the result should still be an equality:
[tex]3 = -3\times 1 + b[/tex].
Solve this equation for [tex]b[/tex]:
[tex]b = 6[/tex].
Thus, the equation of this line would be [tex]y = -3\, x + 6[/tex].
