Question

What is an equation of a line (in slope-intercept form) that passes through the points (4,0) and-2, 1)?

Answer 1

`y=-(x)/(6)+(4)/(6)`

Explanation:

Equation of a line:

The equation of a line, in slope-intercept formula, is given by:

y = mx + b

In which m is the slope and b is the y-intercept.

To find the slope, we select two points. The slope is the change in y divided by the change in x.

In this question:

Points (4,0) and (-2,1) .

Change in y: 1 - 0 = 1

Change in x: -2 -4 = -6

So the slope is:

1/-6 = -1/6

The equation has the format:

y = (-1/6)x + b

Since it passes through the point (4,0), we have that when x = 4, y = 0. So

0 = (-1/6)*4 + b

b - 4/6 = 0

b = 4/6

So the equation of the line is:

`y=-(x)/(6)+(4)/(6)`