The y-intercept of a line that has a slope of –3 and passes through point (–5, 4) is -11.
The slope-intercept of a line is
[tex](y-y_{1})=m(x-x_{1})[/tex]
Here, [tex](x_{1},y_{1})[/tex] is the point through which the line passes and 'm' is the slope of the line.
Given, the line has a slope of –3 and passes through point (–5, 4).
Therefore, [tex](y-4)=-3[x-(-5)][/tex]
⇒ [tex](y-4)= -3(x+5)[/tex]
⇒ [tex](y-4)= -3x-15[/tex]
⇒ [tex]3x+y = -11[/tex]
⇒ [tex]y = -3x-11[/tex]
Comparing it with the standard form of equation, we get:
the y-intercept of the required line is -11.
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