Question

find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.

slope: 0, ordered pair: \\((4, -1)\\)

Explanation:

Identify the given values

We are given the following parameters for the line:

• Slope \(m = 0\)
• A point on the line with coordinates \((x_1, y_1) = (4, -1)\)

Recall the slope-intercept form

Using the Linear Equations in Two Variables concept, the slope-intercept form of a linear equation is:

$$y = mx + b$$

where \(m\) represents the slope and \(b\) represents the \(y\)-intercept.

Substitute the slope and point

Using the Solving Linear Equations concept, we substitute the slope \(m = 0\) and the coordinates of the given point \((4, -1)\) into the slope-intercept equation to solve for \(b\):

$$-1 = 0(4) + b$$

$$-1 = 0 + b$$

$$b = -1$$

Write the final equation

Substitute \(m = 0\) and \(b = -1\) back into the slope-intercept form:

$$y = 0x - 1$$

Simplifying this expression gives:

$$y = -1$$

This represents a horizontal line where the \(y\)-value is always \(-1\).

Answer:

Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.

slope: 0, ordered pair: \((4, -1)\)

<blank>\(y = -1\)</blank>