Parallel Lines
Write the slope of any line parallel to the line y = 2x + 5
y = 2x ______
What is the slope of a line perpendicular to the line y = (1/3)x + 4?
Perpendicular slope = -3
What is the slope of the line through (0, 0) and (3, 6)?
Slope: 2
What is the reciprocal of the slope (3/4)?
Reciprocal: 4/3
Convert 2x + y = 6 into slope-intercept form.
Slope-intercept form: y = -2x + 6
Find the equation in slope-intercept form of the line parallel to y=(-3/4)x + 1 that passes through the point (4, -2).
y=(-3/4)x + 1
Find the equation of the line perpendicular to y = -2x + 6 that passes through (1, 2). Give your answer in slope-intercept form.
Perpendicular slope = 1/2
y = (1/2)x + (3/2)
Find the slope of the line passing through (2, -1) and (7, 4).
Slope: 1
If a line has slope m = (-5/2), what is the reciprocal of m? (Leave answer in fraction)
Reciprocal: -2/5
Rewrite -3x + 4y = 12 in slope-intercept form. Identify the slope and y-intercept.
Slope-intercept form: y = (3/4)x + 3
Slope: 3/4
Y-intercept: (0, 3)
Given line A: 3x - 6y + 9 = 0, write the equation of a line parallel to A that passes through (0, -1). Give your final answer in slope-intercept form.
y = (1/2)x + (3/2)
A line passes through points (2, 3) and (5, 7). Find the equation of the perpendicular to this line that passes through (2, 3).
Slope: 4/3
Perpendicular slope = -3/4
Equation: y = (-3/4)x + (9/2)
A line has slope (-2/3) and passes through (9, 1). What is the equation in slope-intercept form?
Slope-intercept: y = (-2/3)x + 7
Explain why reciprocals are relevant (but not sufficient) when finding slopes of perpendicular lines.
The perpendicular slope is the negative reciprocal of the original slope.
Taking only the reciprocal does not include the needed sign change.
Convert 5x - 10y + 15 = 0 to slope-intercept form and simplify the slope.
Slope-intercept form: y = (1/2)x + (3/2)
Slope: 1/2
Two lines are parallel. One has equation y = (5/2)x - 3. The other passes through (-6, 8). Write the equation of the second line.
y = (5/2)x + 23
Given the line 6x + 2y = 4, find the equation of the line perpendicular to it that passes through (-1, 5).
Slope-intercept form: y = -3x + 2
Perpendicular slope: 1/3
Equation: y = (1/3)x + (16/3)
Determine the slope of the line perpendicular to the line that goes through (1, 2) and (4, -4).
Perpendicular slope: 1/2
Given a nonzero slope m, express the slope of a line perpendicular to a line with slope (-1/m) and simplify.
Perpendicular slope: m
A line is given by 7x + 3y - 21 = 0. Put it into slope-intercept form and state its slope and y-intercept.
Slope-intercept form: y = (-7/3)x + 7
Slope: -7/3
y-intercept: (0, 7)
Determine whether the lines represented by 4x - 2y = 7 and 8x - 4y = -1 are parallel. Justify your answer algebraically.
Both equations have slope = 2. Yes, they are parallel because slopes are equal.
Show algebraically whether the lines y = (4/5)x + 2 and 5x + 4y = 12 are perpendicular. Explain your reasoning and provide the perpendicular equation through the point where they intersect.
1st slope: 4/5
2nd slope: -5/4
Negative reciprocals, lines are perpendicular.
Slope: -5/3
A line has the slope (2/7). Find the negative reciprocal.
Negative reciprocal: -7/2
Convert the standard form equation -8x + 6y = -2 into slope-intercept form. Then determine the equations of both a line parallel and a line perpendicular to it that pass through the point (1, 4).
Slope-intercept form: y = (4/3)x - (1/3)
Parallel: y = (4/3)x + (8/3)
Perpendicular: y = (-3/4)x + (19/4)