Answer:
a.y=13/16x+37/8
b.y=3/2x+6
c.y=3/4x+9/2
d.x=-2
Step-by-step explanation:
All lines must pass through (-2,3)
a. The slope must be 13/16;
y=13/16x+b, SInce it must pass through (-2,3), plug in -2 as the x-value and 3 as the y-value
3=13/16(-2)+b, solve for b.
24/8=-13/8+b
37/8=b
y=13/16x+37/8
b, It must be parallel to the line 3x-2y=2; first, find the slope by converting to y=mx+b
3x-2y=2
-2y=-3x+2
y=3/2x-1, Parallel lines have the same slope so a line parallel to 3x-2y=2 and passing through (-2,3) will have a slope of 3/2.
Plug in (-2,3) to find the b-value again.
(3)=3/2(-2)+b
3=-3+b
6=b
y=3/2x+6
c. It must have a line perpendicular to 4x+3y=6. Again like in b, find the slope.
y=-4/3+2, the slope is -4/3.
Now, perpendicular lines have the opposite inverse slopes which means that you add a negative sign and flip the numerator and denominator
-(-3/4), this is just 3/4
Ok, the slope of the line is 3/4, plug in (-2,3) to find the b-value again.
(3)=3/4(-2)+b
6/2=-3/2+b
9/2=b
y=3/4x+9/2
d. The line is paralell to the y-axis.
This just means that the line is vertical. The line has no slope.
The vertical line that passes through the x-value -2 is x=-2
x=-2
