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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
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.
Aug 24, 2022 · How to find an equation of a line parallel to a given line. Find the slope of the given line. Find the slope of the parallel line. Identify the point. Substitute the values into the point-slope form: \(y−y_1=m(x−x_1)\). Write the equation in slope-intercept form. How to find an equation of a line perpendicular to a given line
Answer. To determine if the lines are parallel or perpendicular, we first want to find their slopes. We can do this by writing both equations in the form 𝑦 = 𝑚 𝑦 + 𝑐, where 𝑚 is the slope and 𝑐 is the 𝑦 -intercept. The first equation is already in this form, so it has slope 1 7.
Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. In other words, if m = a b, then m ⊥ = − b a. To find an equation of a line, first use the given information to determine the slope. Then use the slope and a point on the line to find the equation using point-slope form.
Writing Equations of Parallel Lines. If we know the equation of a line, we can use what we know about slope to write the equation of a line that is either parallel or perpendicular to the given line. Suppose we are given the following function: [latex]f\left(x\right)=3x+1[/latex] We know that the slope of the line is 3.
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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.
