Question

Write an equation for a line passing through the point (4,a) and (-5,a)

Answer 1

The equation of the line is

y = a

Step-by-step 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

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For this question,

(x₁, y₁) and (x₂, y₂) are (4, a) and (-5, a)

`\text{Slope = }(a-a)/(-5-4)=(0)/(-9)=0`

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!!!