Respuesta :
Answer
The equation of the line is
y = a
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
So, we just need to calculate the slope and use one of the points to calculate this equation of the line
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (4, a) and (-5, a)
[tex]\text{Slope = }\frac{a-a}{-5-4}=\frac{0}{-9}=0[/tex]Using (4, a) as the point,
Recall,
y - y₁ = m (x - x₁)
m = 0
(x₁, y₁) = (4, a)
x₁ = 4
y₁ = a
y - y₁ = m (x - x₁)
y - a = 0 (x - 4)
y - a = 0
y = 0 + a
y = a
Hope this Helps!!!
