HOMEWORK 9
RICKY NG
Question 9.1. Negative slope.
Question 9.2. Vertical line has slope undefined.
Question 9.3. Find the slope for the line passing through (8, −7) and (−1, −7)
Solution. Recall that
m=
So
m=
y2 − y1
.
x 2 − x1
0
−7 − (−7)
=
= 0.
−1 − 8
−9
Question 9.4. Find the slope for the line passing through (1, −4) and (−7, 2)
Solution. Just as previous question,
2 − (−4)
2+4
=
−7 − 1
−8
6
2×3
=
=−
−8
2×4
3
=− .
4
m=
7
) and ( 14 , − 87 )
Question 9.5. Find the slope for the line passing through (− 53 , − 10
Solution. Let’s solve it step-by-step: Since lcm(8, 10) = 40,
7
7
7
7
y2 − y1 = − − −
=− +
8
10
8 10
7 5
7 4
−35 28
=− × + × =
+
8 5 10 4
40
40
7
=− .
40
Similarly, lcm(5, 4) = 20, so
1
3
1 3
x2 − x1 = − −
= +
4
5
4 5
1 5 3 4
5
12
= × + × =
+
4 5 5 4
20 20
17
= .
20
1
Finally,
y2 − y1
x2 − x1
−7
7
17
= 1740 = − ÷
40 20
20
20
7
20 · 1
7
=−
×
=− ×
40 17
20 · 2
17
7×1
7
=−
=− .
2 × 17
34
m=
Question 9.6. x-intercept is where the line hits the x-axis. So from the graph, this is
when x = −4, or equivalently, the point (−4, 0).
Question 9.7. y-intercept is where the line hits the y-axis. So from the graph, this is
when y = 5, or equivalently, the point (0, 5).
Question 9.8. Find the slope of the line above.
Solution. Recall that we can pick any two distinct points of the line. Here I choose
(−4, 0) and (0, 5) (as we found already). Hence,
y2 − y1
5−0
5
m=
=
= .
x2 − x1
0 − (−4)
4
Question 9.9. Find the x-intercept of the line
y = 3x + 6
Solution. For x-intercept, we let y = 0:
3x + 6 = 0
3x = −6
x = −2.
Hence, the point is (−2, 0).
2
Question 9.10. Find the y-intercept of the line
4x + 6y = −9
Solution. For y-intercept, let x = 0:
4(0) + 6y = −9
6y = −9
3
−9
=− .
y=
6
2
So the point is 0, − 23 .
3