Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope.
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We have the equation of the line: [tex]y=-\dfrac{3}{4}x-5[/tex]
The slope is [tex]m=-\dfrac{3}{4}[/tex].
Put the value of the slope and the coordinates of the point (4, -6) to an equation of a line:
[tex]-6=-\dfrac{3}{4}(4)+b[/tex]
[tex]-6=-3+b[/tex] add 3 to both sides
[tex]-3=b\to b=-3[/tex]
Finally:
[tex]y=-\dfrac{3}{4}x-3[/tex]
