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.
Passing through $(1,2)$ and $(5,10)$

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Key Concepts

Slope of a Line

The slope of a line measures its steepness and direction. It is calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run) between two points on the line. This value is essential in various forms of linear equations, as it directly influences the line's orientation in the coordinate plane.

Point-Slope Form

The point-slope form is a method to express the equation of a line when given a specific point on the line and its slope. It is typically written as y - y? = m(x - x?), where (x?, y?) is a point on the line and m is the slope. This form is particularly useful for quickly setting up the equation of a line and is a stepping stone to converting into other forms, such as the slope-intercept form.

Slope-Intercept Form

The slope-intercept form of a line is a widely used format expressed as y = mx + b. In this equation, m represents the slope of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis. This form provides a clear understanding of the line's behaviour by directly indicating its rate of change and its starting value on the y-axis.

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