Hello Ayriel.
I thought it best to copy your entire question in my response and answer one part at a time.
y+4=-4(x-2)
1. What is the slope of the given line? The slope is -4, which is the coefficient of x
2. What point does this line pass through, which is the basis of this equation? To determine the point the line passes through. Recall the basic form of the point slope equation. y-y1=m(x-x1). The point is (x1,y1), which in this case is (2,-4). Notice it's -4 since we have y+4 and the general form of the equation is y-y1.
3. Rewrite this equation in slope-intercept form.
1. What is the slope of the given line? The slope is -4, which is the coefficient of x
2. What point does this line pass through, which is the basis of this equation? To determine the point the line passes through. Recall the basic form of the point slope equation. y-y1=m(x-x1). The point is (x1,y1), which in this case is (2,-4). Notice it's -4 since we have y+4 and the general form of the equation is y-y1.
3. Rewrite this equation in slope-intercept form.
y+4=-4(x-2)
distribute the slope (-4)
y+4=-4x+8
y+4=-4x+8
Subtract 4 from both sides
y = -4x+4
4. What is the y-intercept of this line? The y-intercept is determined from the slope intercept form in 3 above. This line crosses the y axis at +4. Expresses as a point on a coordinate plane, we have (0,4).
5.Rewrite this equation in standard form.
With standard form, both x and y are on the same side of the equation.
y = -4x+4
Add 4x to both sides
4x+y=4
6. What is the x-intercept of this line? The x-intercept is where the line crosses the x-axis, in other words, where y = 0. Using the equation above, when y=0, x=1. 1 is the x-intercept. Expressed as a point, we have (1,0).
7. What is the equation in standard form of a perpendicular line that passes through (5, 1)? A perpendicular line has a slope that is the negative inverse of the given line. Since the slope of the original line is -4, the slope of the line perpendicular to it is +1/4. Using the point slope form given in question 2, we have
6. What is the x-intercept of this line? The x-intercept is where the line crosses the x-axis, in other words, where y = 0. Using the equation above, when y=0, x=1. 1 is the x-intercept. Expressed as a point, we have (1,0).
7. What is the equation in standard form of a perpendicular line that passes through (5, 1)? A perpendicular line has a slope that is the negative inverse of the given line. Since the slope of the original line is -4, the slope of the line perpendicular to it is +1/4. Using the point slope form given in question 2, we have
y-1 = (1/4)(x-5)
y-1 = (1/4)x - 5/4
y = (1/4)x -1/4
y = x/4 - 1/4
8. What is the x-intercept of the perpendicular line? The x-intercept is when y=0. In order for y to = 0, x must be 1. The x-intercept is 1 (1,0).
Use the point-slope form linear equation given to complete those problems 1-8 that you did.
9. What is the equation in standard form of a parallel line that passes through (0, -2)? A parallel line has the same slope (-4). Using the point (0,-2) and the slope -4
8. What is the x-intercept of the perpendicular line? The x-intercept is when y=0. In order for y to = 0, x must be 1. The x-intercept is 1 (1,0).
Use the point-slope form linear equation given to complete those problems 1-8 that you did.
9. What is the equation in standard form of a parallel line that passes through (0, -2)? A parallel line has the same slope (-4). Using the point (0,-2) and the slope -4
y+2 = -4(x-0)
Working through this equation
y+2 = -4x
y = -4x-2 slope intercept form
4x + y = -2 standard form
10. On the parallel line, find the ordered pair where x=-2
When x=-2, y = (-4)(-2) - 2
y = 8-2 = 6
The ordered pair is (-2,6)
11. Graph the original equation that was given. Include your point from problems 2,3, and 4, labeled A,B, and C, respectively. I'll leave the graph to you. Note however that the y-intercept is 8 and the slope is -4
12. Add the perpendicular line to your graph. Include the point given in problem 7 and your point from problem 8, labeled P and Q respectively. Leaving this to you.
13. Add the parallel line to your graph. Include the point given in problem 9 and your point from problem 10 labeled L and M respectively. Leaving this to you.
14. Describe the relationship (if any) between the lines drawn in problem 12 and 13. You should notice that the parallel line added in item 13 is perpendicular to the line added in item 12. If two lines are parallel, then a line perpendicular to one is perpendicular to the other.
11. Graph the original equation that was given. Include your point from problems 2,3, and 4, labeled A,B, and C, respectively. I'll leave the graph to you. Note however that the y-intercept is 8 and the slope is -4
12. Add the perpendicular line to your graph. Include the point given in problem 7 and your point from problem 8, labeled P and Q respectively. Leaving this to you.
13. Add the parallel line to your graph. Include the point given in problem 9 and your point from problem 10 labeled L and M respectively. Leaving this to you.
14. Describe the relationship (if any) between the lines drawn in problem 12 and 13. You should notice that the parallel line added in item 13 is perpendicular to the line added in item 12. If two lines are parallel, then a line perpendicular to one is perpendicular to the other.
Ayriel H.
You explained really well! I was able to understand it and it helped a lot!
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02/23/16
Ayriel H.
02/23/16