Write an equation of the line satisfying the given...

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form or
standard form.
The line contains the point $(-1,4)$ and is parallel to a line with a slope of $\frac{1}{2}$.

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Key Concepts

Slope

The slope is a measure of the steepness or incline of a line and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It indicates how much the y-value changes for a unit change in the x-value.

Parallel Lines

Parallel lines are lines in the same plane that never intersect. In the context of linear equations, parallel lines have the same slope, which is a key property used to determine if two lines are parallel.

Point-Slope Form

The point-slope form is an equation of a line that uses a known point on the line and the slope. It is written as y - y? = m(x - x?) and is particularly useful for writing the equation of a line when a point and the slope are given.

Slope-Intercept Form

The slope-intercept form of a line is written as y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful for quickly graphing the line and understanding its behavior in terms of how steep it is and where it crosses the y-axis.

Standard Form

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers, and A is usually non-negative. This form is useful for algebraic manipulations and sometimes for finding intercepts by comparison.

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