Consider the linear equation y = 20x 59.

Question

Select all the statements that are true.
the slope of the line is 59.
the slope of the line is 20.
the x intercept is 59.
the y intercept is 59.
The equation y - 59 = 20(x - 0) is equivalent to the given equation.
the equation 20x + y = 59 is equivalent to the given equation.

Answer 1

Let's analyze the given linear equation \( y = 20x + 59 \).

1. The slope of the line is 59.

   • False. The slope is the coefficient of \( x \), which is 20.

2. The slope of the line is 20.

   • True. The slope is indeed 20.

3. The x intercept is 59.

   • False. To find the x-intercept, set \( y = 0 \): \[ 0 = 20x + 59 \implies 20x = -59 \implies x = -\frac{59}{20} \] Therefore, the x-intercept is \(-\frac{59}{20}\), not 59.

4. The y intercept is 59.

   • True. The y-intercept is the constant term in the equation, which is 59 when \( x = 0 \).

5. The equation \( y - 59 = 20(x - 0) \) is equivalent to the given equation.

   • True. This equation simplifies to \( y = 20x + 59 \), which is equivalent to the original equation.

6. The equation \( 20x + y = 59 \) is equivalent to the given equation.

   • False. Rearranging \( 20x + y = 59 \) gives \( y = -20x + 59 \), which is not equivalent to \( y = 20x + 59 \).

Summarizing the true statements:

• The slope of the line is 20.
• The y intercept is 59.
• The equation \( y - 59 = 20(x - 0) \) is equivalent to the given equation.