Question

A straight line passes through the points (1,3) and (2,2). What is the x-intercept of this line?

Answer 1

Answer:

x-int: (4, 0)

Step-by-step explanation:

First, we need to find the equation of the line.

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

Thus, we need to find the slope first by using the slope formula:

$\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ or change in y / change in x

So we have: $\frac{3-2}{1-2}=\frac{1}{-1}=-1=m$

We must plug in the slope to find the y-intercept:

$3=-1(1)+b\\3=-1+b\\4=b$

So the equation of the line is y = -x + 4

The x-intercept means that the y coordinate is 0 so we can use the equation:

$0=-x+4\\-4=-x\\4=x$