Question

Write an equation in slope-intercept form of each line described. Horizontal line through (8,-4)

Answer 1

y = -4

Explanation:

Horizontal line means the slope is 0.

Since the coordinate given is 8,-4 we know that the line passed through a x - coordinate of 8 and a y-coordinate of -4.

This would mean one straight line passing through -4 on the y-axis which would give the equation:

y = -4

To make sure:

Horizontal line = 0

So, slope = 0

Let's use the point-slope formula now:

y - y1 = m(x - x1)

Given coordinate = (8, - 4)

Plug in slope and coordinate:

y - (-4) = 0(x - 8)

y + 4 = 0

-4 -4

y = -4

The answer is y = -4.

Answer 2

`\textsf{The equation of the horizontal line in slope-intercept form is: } \boxed{\sf y = -4}`

Explanation:

A horizontal line has a constant y-coordinate, meaning its slope is 0. The slope-intercept form of a linear equation is given by:

`\sf y = mx + b`

Where:

• y is the y-coordinate of a point on the line,
• m is the slope of the line,
• x is the corresponding x-coordinate,
• b is the y-intercept of the line.

Since the slope of a horizontal line is 0, the equation simplifies to:

`\sf y = b`

Given that the line passes through the point (8, -4), we can substitute these values to find b.

`\sf -4 = b`

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

`\boxed{\sf y = -4}`