Write the point-slope form of the equation of the line...

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises $1-28 .$ Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope $=\frac{1}{2},$ passing through the origin

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Key Concepts

Point-Slope Form

The point-slope form is a way to write the equation of a line when you know one point on the line and its slope. It is given by the formula (y - y?) = m(x - x?), where m represents the slope and (x?, y?) is a specific point on the line. This form is particularly useful for quickly formulating the equation of a line from minimal information.

Slope-Intercept Form

The slope-intercept form expresses a linear equation in the format y = mx + b, where m is the slope and b is the y-intercept, which is the point where the line crosses the y-axis. This form is advantageous for graphing a line and for easily identifying the slope and y-intercept directly from the equation.

Slope

The slope is a measure of the steepness and direction of a line, defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It is a fundamental concept in linear equations because it determines how fast the y-value changes with respect to changes in the x-value.

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