Page 25 - Algebra

Explanation:
1. Slope or m of the line passing through
2. Slope or m of the line passing through
3. To calculate the x-intercept, put y = 0, and solve for x. 8x – 3(0) + 24 = 0
8x = –24
x = –3
4. Slope or m of the line passing through
Slope of line passing through (–6, –3) and (1, 4)
x1 = –6 x2 = 1
m=𝑦2−𝑦1 = 4−(−3)=7=1 𝑥2− 𝑥1 1−(−6) 7
Slope of line passing through (0, 6) and (– 9, 3)
m====
𝑥2− 𝑥1 −9−0 −9 3
k =3
5. The point-slope form of an equation is given by: y–y1 =m(x–x1)
The line passes through (–7, 3) and (2, –6)
–6
Put m in y – y1 = m(x – x1) y – 3= – 1(x + 7)
(x1, y1) and (x2, y2) = 𝑦2− 𝑦1 𝑥2− 𝑥1
y1 = – 3 y2 = 4
(x1, y1) and (x2, y2) = 𝑦2− 𝑦1 𝑥2− 𝑥1
y1 = 6 y2 = 3
x1 = 0 x2 = – 9
𝑦2−𝑦1 3−6 −3 1
(x1, y1) and (x2, y2) = 𝑦2− 𝑦1 𝑥2− 𝑥1
Slope of line passing through (5, k) and (k, –5)
y1 = k y2 =–5
x1 = 5 x2 = k
4 = 𝑦2− 𝑦1 𝑥2− 𝑥1
−5−𝑘 4= 𝑘−5
4(k – 5) = –5 – k
4k – 20 = –5 – k
5k = 15
y1 = 3 y2 =
x1 = –7 x2 = 2
−6−3 −9 m=2−(−7)= 9 =–1
Page 24 of 177
Algebra I & II