a. Equation in slope-intercept form of a line parallel to y = 2/5x +1 will be: y = 2/5x + 5
b. Equation in slope-intercept form of a line perpendicular to y = 2/5x +1 will be: y = -5/2x + 1
c. Equation in slope-intercept form of a line that is neither parallel nor perpendicular to y = 2/5x +1 will be: y = 3x + 1
<h3>Slope-intercept Equation of Parallel and Perpendicular Lines</h3>
- Slope-intercept equation, where b is the y-intercept and b m is the slope is represented as y = mx + b.
- Equations of parallel lines have the same slope.
- Equations of perpendicular lines will have slope that are negative reciprocal of each other.
- If two lines are neither parallel nor perpendicular, their equation will have different slopes, and the slope of one is not the negative reciprocal of each other.
Therefore:
a. Equation in slope-intercept form of a line parallel to y = 2/5x +1 will be: y = 2/5x + 5
b. Equation in slope-intercept form of a line perpendicular to y = 2/5x +1 will be: y = -5/2x + 1
c. Equation in slope-intercept form of a line that is neither parallel nor perpendicular to y = 2/5x +1 will be: y = 3x + 1
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