Question

Write an equation that passes through the points (0,-5) and (8,-5)

Answer 1

Answer:

Equation of the line: $y = -5$.

Step-by-step explanation:

Let $(x_0,\, y_0)$ and $(x_1,\, y_1)$ denote the coordinates of these two points, respectively.

Calculate the slope $m$ of this line:

$\displaystyle m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{(-5) - (-5)}{8 - 0} = 0$.

Notice that the slope is zero because the two points have the same $y$-coordinates ($y_0 = y_1 = -5$) even though their $x$-coordinates are distinct ($x_0 \ne x_1$.)

Equation for this line in point-slope form:

$y - y_0 = m\, (x - x_0)$.

$y - (-5) = 0\, (x - 0)$.

Rewrite and simplify to obtain the equation of this line in slope-intercept form:

$y = -5$.

The $x$-term was eliminated because the slope was zero.