Write the slope-intercept equation of the line that passes through the given point and that is p

step 1 We need to write the equation of a line in slope intercept form that passes to the given point a

Write the slope-intercept equation of the line that passes...

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Key Concepts

Converting Equation Forms

Converting an equation from one form to another, such as from a fractional or standard form to the slope-intercept form, involves algebraic manipulation to isolate y. This process allows one to easily identify the slope and y-intercept, which are essential for understanding the line's characteristics and relationship with other lines.

Point-Slope Form

The point-slope form is a method for writing the equation of a line when you know a point on the line and its slope. It is written as y - y? = m(x - x?), where (x?, y?) is the known point. This form is especially useful for deriving an equation before converting it into slope-intercept form.

Parallel Lines

Parallel lines are defined as lines in the same plane that never intersect, which means they must have identical slopes. This property allows one to determine the slope of a new line that is parallel to a given line, ensuring both lines maintain the same angle of inclination.

Slope-Intercept Form

The slope-intercept form of a line is expressed as y = mx + b, where m represents the slope and b is the y-intercept. This form is widely used because it directly shows the line's steepness and where it crosses the y-axis, facilitating graphing and comparison with other lines.

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