1)
[tex]y=mx+b[/tex]
where m is the slope
We know the slope is 5 and the line passes through the point (4,3).
[tex]m=5 \\
(4,3) \\
x=4 \\ y=3 \\ \\
3=5 \times 4 + b \\
3=20 + b \\
b=3-20 \\
b=-17[/tex]
The equation of the line is:
[tex]y=5m-17[/tex]
Now the second point:
[tex](2,y) \\
x=2 \\
y \\ \\ y=5 \times 2 -17 \\ y=10-17 \\ y=-7[/tex]
The answer:
The value of y is -7.
2)
The line passes through the origin, or the point (0,0), and has a slope of -32.
The slope is negative so the line goes down from left to right.
It crosses both x and y axes in the point (0,0).
Therefore, it only passes through II and IV quadrant.
You can also find the equation of the line, find one more point and draw it.
[tex]y=mx+b \\ \\
m=-32 \\
(0,0) \\
x=0 \\ y=0 \\ \\
0=-32 \times 0 + b \\
b=0 \\ \\
y=-32x[/tex]
Find the y-coordinate of the point for example (1,y).
[tex](1,y) \\
x=1 \\ y \\ \\
y=-32 \times 1 \\
y=-32[/tex]
The line passes through the points (0,0) and (1,-32). Now you can draw it (see the attachment).
The answer:
The line passes through quadrants II and IV.
