Answer:
Two lines that pass through the point (4, 8) are y = 3·x - 4 and y = -5·x + 28
Explanation:
The equation of two lines that passes through the point (4, 8) are found using the general form of a straight line equation, y = m·x + c, where;
m = The slope of the line
c = The y-intercept
Therefore, two distinct line pass through a given point if they have a different slope, m, and a different y-intercept, c, as follows;
Fot the given point, the x-value = 4, and the y-value = 8, we get;
8 = m₁·4 + c₁...Line 1 and
8 = m₂·4 + c₂...Line 2
m₁ ≠ m₂
If we set m₁ = 3, for line 1, we get;
8 = 3 × 4 + c₁ = 8 = 12 + c₁
∴ c₁ = 8 - 12 = -4
c₁ = -4
The equation for Line 1 for all x and y-values, where, m₁ = 3, c₁ = -4, becomes;
y = 3·x - 4
The equation for Line 2 where m₂ = -5 for example, we have;
8 = -5 × 4 + c₂
∴ c₂ = 8 + 5 × 4 = 28
c₂ = 28
The general form for the equation for Line 2 becomes;
y = -5·x + 28
Therefore;
The equation of the two formed lines that pass through the point (4, 8) are;
y = 3·x - 4 and y = -5·x + 28