Algebra Slope Intercept - find the equation

Question

Find the equation of the line that passes through the coordinates (-3,5) and (-3,4)

My book says the answer is x= -3 but I don't know how or why

Answer 1

Both points have the same x-coordinate. The line is vertical. That means every point on that vertical line has the same x-coordinate (-3). We say that vertical lines do not have a slope (or the slope is undefined). Vertical lines have equations of the form x = c where c is a constant.

Horizontal lines have equations of the form y = k where k is a constant.

Check out this graph on Desmos and see if that graph helps clear this up for you.

desmos.com/calculator/3khqc4bgqs

You can visit the graph by selecting the above URL,, right-clicking and choosing "Go to...".

Answer 2

x= -3 is the equation of the line through any two points that have the same x coordinate

whether its' (-3,5) and (-3,4) or (-3, any other y value)

Answer 3

According to slope (m), y2-y1/x2-x1=4-5/-3-(-3).

m=-1/0, which shows that the slope of line is undefined also says Infinity. Because, whenever Real number divide by zero, the result would be infinity.

And also the coordinates is telling the value of x in both coordinate is similar. Which means line in parallel to y-axis.

In that case the general formula of line parallel to y-axis is, x=x1.

So, the equation of line is x=-3.