Question

Write an equation of the line through (5,0) and (-1,0) in slope-intercept form.

Answer 1

See Below

Explanation:

To write the equation of the line through the points (5,0) and (-1,0) in slope-intercept form (y = mx + b), we first need to find the slope (m) of the line.

The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:

• m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the given points, we get:

• m = (0 - 0) / (-1 - 5) = 0

Since the y-coordinates of both points are 0, the line is a horizontal line and the slope is 0.

To find the y-intercept (b) of the line, we can choose either of the given points and substitute the values of the slope and the coordinates into the slope-intercept form equation:

• y = mx + b

We'll choose the point (5,0):

• 0 = 0(5) + b

• b = 0

Therefore, the y-intercept of the line is 0.

So, the equation of the line in slope-intercept form is:

• y = 0x + 0

which simplifies to:

• y = 0

In other words, the equation of the line passing through the points (5,0) and (-1,0) is y = 0, which represents a horizontal line on the x-axis.

Answer 2

y = 0

Explanation:

The first step is to find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

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

= 0/-6

= 0

The slope is zero

Using the slope intercept form

y = mx+b

y = 0x+b

The y value is 0

0 = 0+b

b is 0

y = 0