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Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2. We can solve it by using the "point-slope" equation of a line: y − y1 = 2 (x − x1) And then put in the point (5,4): y − 4 = 2 (x − 5)
- Slope
- −0.5
A General Note: Parallel and Perpendicular Lines. Two lines are parallel lines if they do not intersect. The slopes of the lines are the same. f (x) =m1x+b1 and g(x) =m2x+b2 are parallel if m1 = m2 f (x) = m 1 x + b 1 and g (x) = m 2 x + b 2 are parallel if m 1 = m 2. If and only if b1 = b2 b 1 = b 2 and m1 = m2 m 1 = m 2, we say the lines ...
Parallel Lines. Perpendicular Lines. Parallel lines are those that never intersect and are always the same distance apart. Perpendicular lines are those that always intersect each other at right angles. Perpendicular lines are denoted by the symbol ⊥. The symbol || is used to represent parallel lines.
Answer: The first step is to write the equation in slope-intercept form. We see that the slope is m=\frac {5} {3} m = 35. This means that the slope of the line perpendicular to the given line is the negative reciprocal or -\frac {3} {5} −53. Next, we use point-slope form with this new slope and the given point.
Rule. Find the value of the slope perpendicular to the straight line by applying the following formula: m1 ×m2 = −1 m 1 × m 2 = − 1 where m1 m 1 is the slope of the given perpendicular line and m2 m 2 is the slope of the line for which we are looking for the equation. In the equation y = mx+b y = m x + b, replace the parameter m m with ...
Second: Be familiar with the two (2) most useful forms of the line, namely: Slope Intercept Form and Point Slope Form. Note: Two lines on the same plane are parallel if they have the same distance and will never meet or will never intersect. Two lines on the same plane are perpendicular if they intersect or meet at a 9 0 ∘ 90^\circ degree angle.
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Problem Solving. In some problems, we may be given properties of the slopes and intercepts of two lines and wish to calculate the values for the slopes and intercepts. Consider two lines y=-2x+3 y = −2x +3 and y= (K+1)x+4. y = (K +1)x+ 4. When K=a, K = a, the two lines are parallel. When K=b, K = b, the two lines are perpendicular.
