Page 31 - Algebra

Explanation:
1. Theequationofx-axisisy=0ory =0x+0 The slope of the line is 0.
Use the point-slope form
y–y1 =m(x–x1)
y – 8 = 0(x + 2) y–8=0
y=8
2. The equation of y-axis is x = k
It’s a vertical line.
Here k is the x-coordinate of the point through which the line passes. Therefore, the equation of the line which passes through (4, – 4) is x = 4
3. The two roads will never meet each other when they are parallel to each other. Equation of the first road is y = 2x – 3
Slope = 2
The equation of the new parallel road will also be 2.
Using the point-slope form y–y1 =m(x–x1)
y – 1 = 2(x + 4)
y – 1 = 2x + 8
y = 2x + 9
4. The two roads meet perpendicular to each other. Equation of the first road is y = 2x – 3
Slope = 2
Product of slopes of two perpendicular lines is –1
m1m2 =–1 2m2 = –1
1 2
Using the point-slope form y–y1 =m(x–x1)
1
y–1=– (x+4)
2
2y – 2 = – x – 4 2y = – x – 2
5. All parallel lines have the same slope. Slope of line passing through
m2 = –
9+1 = 4−𝑏 4+ 6 11−1
10 =4−𝑏 10 10
10 = 4 – b
b = –6
(x1, y1) and (x2, y2) = 𝑦2− 𝑦1 𝑥2− 𝑥1
Page 30 of 177
Algebra I & II