Suppose that a line passes through the points (-5,-1) and (0,1). Where will it pass through the x-axis.

Question

Suppose that a line passes through the points (-5,-1) and (0,1). Where will it pass through the x-axis.

 

The graph will pass through the X-axis at 

Answer 1

The easiest way to find where the graph will pass through the x axis is to find the equation of the line.

The standard form of a line is:

y = mx + b

where m is the slope and b is the y intercept.

The slope of a line is the change in y over the change in x between two points, so the slope of this line using the two given points is:

m = (-1-1)/(-5-0)
m = -2/-5
m = 2/5

We can plug this slope into the standard form like this:

y = mx + b
y = (2/5) + b

To find the y intercept, we can plug in either of the two points into the standard equation and solve for b. Lets use the point (0,1).

1 = (2/5)*0 + b
1 = 0 + b
b = 1

The equation of the line is:

y = (2/5)x + 1

The line intersects the x axis when y = 0. Plug y = 0 into the equation of the line:

0 = (2/5)x + 1
-1 = (2/5)x
-5 = 2x
x = -2/5

The graph intersects the x axis at x = -2/5.