Question

Write the equation of the line in slope-intercept form that passes through the point (−,) and is parallel to =− .

Answer 1

The equation of the line in slope-intercept form that passes through the point
`\((x_1, y_1)\)` and is parallel to
`\(y = mx + b\)` is
`\(y = mx_1 + (y_1 - mx_1)\).`

Step-by-step explanation:

To find the equation of a line parallel to
`\(y = mx + b\)` , we know that the slopes of the two lines must be equal. The slope-intercept form of a line is
`\(y = mx + b\),` where
`\(m\)` is the slope. So, for the parallel line, the slope remains
`\(m\).` Now, we have the point
`\((x_1, y_1)\)` through which our parallel line passes.

The equation
`\(y = mx_1 + (y_1 - mx_1)\)` represents the line in slope-intercept form. Here,
`\(mx_1\)` is the term representing the slope, and
`\((y_1 - mx_1)\)` accounts for the y-intercept. This ensures that the line not only has the required slope but also passes through the specified point.

In this case, the given line is
`\(y = mx + b\)` , and we want a line parallel to it passing through the point
`\((x_1, y_1)\)` . Therefore, the equation of the line in slope-intercept form is
`\(y = mx_1 + (y_1 - mx_1)\)` . This equation allows us to efficiently find the equation of a parallel line while ensuring it passes through the specified point.