Answer:
Step-by-step explanation:
To prove: The sum of a rational number and an irrational number is an irrational number.
Proof: Assume that a + b = x and that x is rational.
Then b = x – a = x + (–a).
Now, x + (–a) is rational because addition of two rational numbers is rational (Additivity property).
However, it was stated that b is an irrational number. This is a contradiction.
Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.
Hence, the sum of a rational number and an irrational number is irrational.
Step-by-step explanation:
Answer:
g
Step-by-step explanation:
Answer:
y = -7/5x
Step-by-step explanation:
First, we need to use the two points to find the slope.
m = y₁ - y₂ / x₁ - x₂
m = -7 - 0 / 5 - 0
m = -7/5
Now we know that the slope is -7/5. Now we'll substitute the information we've gathered into the point-slope form equation to get an equation.
y - y₁ = m(x - x₁)
y - (-7) = -7/5(x - 5)
y + 7 = -7/5x + 7
y = -7/5x
Therefore, the equation of the line is y = -7/5x.