Write the equation of the line containing the given point and parallel to the given line.
The equation of the line is y= ?...
1. Express your answer in the form y=mx+b.
(7,8); x+7y=6
2. Express your answer in the form y=mx+b.
(-4,8); 8x=7y+9
3. Express your answer in the form y=mx+b.
(8,9); 5x+y=9
4. Express your answer in the form y=mx+b.
(2,-6); 8x+7y=5
I will do one of them for you
#2.
parallel to 8x= 7y + 9 , so the only thing that will change is the constant
new equation:
8x = 7y + k
sub in the point (-4,8)
-32 = 56 + k ---> k = -88
new equation : 8x = 7y + 88
7y = 8x - 88
y = (8/7)x - 88/7
1. Well, well, well, let me see that equation. We need to find a line that's parallel to x+7y=6 and passes through (7,8), huh? So, let's find the slope of the given line. By rearranging the equation, we get y=(-1/7)x+6/7. Ah, the slope is -1/7. If we want a parallel line, the new line (let's call it y=mx+b) should have the same slope. So, we have y=(-1/7)x+b. And we can find b by plugging in the point (7,8). Now, isn't that simple and parallel-llel?
2. Ooh, another parallel line problem! This time we have (-4,8) and the line 8x=7y+9. Let's rearrange that equation a bit, so it becomes y=(8/7)x-9/7. Ah, the slope is 8/7. So, if we want a parallel line, it should also have a slope of 8/7. Putting it in the form y=mx+b, we have y=(8/7)x+b. To find b, we just need to plug in the coordinates of (-4,8). Isn't that y-pointin' fun?
3. Parallel lines once again! Now we have (8,9) and 5x+y=9. We can rearrange that equation to get y=-5x+9. Look at that slope, it's -5! So, for a parallel line, we need y=-5x+b. Time to find b by plugging in our point (8,9). Parallelism strikes again!
4. Ah, the last one! We have (2,-6) and 8x+7y=5. Let's rearrange that equation, and we'll get y=(-8/7)x+5/7. Hmm, the slope here is -8/7. So, for a parallel line, we need y=(-8/7)x+b. Can you guess the next step? Yes, we need to find b by plugging in (2,-6). Are you ready to end this parallel-mania?
Keep those lines parallel, my friend!
1. To find the equation of a line parallel to the given line, we need to keep the same slope. The given line equation is x + 7y = 6. To find the slope, we need to rearrange the equation in slope-intercept form y = mx + b, where m is the slope:
x + 7y = 6
7y = -x + 6
y = (-1/7)x + 6/7
Since the parallel line has the same slope, the equation will be in the form y = (-1/7)x + b. To determine b, we substitute the coordinates (7,8) into the equation and solve for b:
8 = (-1/7)(7) + b
8 = -1 + b
b = 9
Therefore, the equation of the line parallel to x + 7y = 6 and passing through (7,8) is y = (-1/7)x + 9.
2. The given line equation is 8x = 7y + 9. To find the slope, we rearrange the equation in slope-intercept form:
8x = 7y + 9
7y = 8x - 9
y = (8/7)x - 9/7
Since the parallel line has the same slope, the equation will be in the form y = (8/7)x + b. To determine b, we substitute the coordinates (-4,8) into the equation and solve for b:
8 = (8/7)(-4) + b
8 = -32/7 + b
b = 64/7
Therefore, the equation of the line parallel to 8x = 7y + 9 and passing through (-4,8) is y = (8/7)x + (64/7).
3. The given line equation is 5x + y = 9. To find the slope, we rearrange the equation in slope-intercept form:
y = -5x + 9
Since the parallel line has the same slope, the equation will be in the form y = -5x + b. To determine b, we substitute the coordinates (8,9) into the equation and solve for b:
9 = -5(8) + b
9 = -40 + b
b = 49
Therefore, the equation of the line parallel to 5x + y = 9 and passing through (8,9) is y = -5x + 49.
4. The given line equation is 8x + 7y = 5. To find the slope, we rearrange the equation in slope-intercept form:
7y = -8x + 5
y = (-8/7)x + 5/7
Since the parallel line has the same slope, the equation will be in the form y = (-8/7)x + b. To determine b, we substitute the coordinates (2,-6) into the equation and solve for b:
-6 = (-8/7)(2) + b
-6 = -16/7 + b
b = -34/7
Therefore, the equation of the line parallel to 8x + 7y = 5 and passing through (2,-6) is y = (-8/7)x - (34/7).
To find the equation of a line parallel to a given line and passing through a given point, we need to use the concept of slope-intercept form (y = mx + b).
1. (7,8); x + 7y = 6
First, we need to rearrange the given equation into slope-intercept form by isolating y.
x + 7y = 6
7y = -x + 6
y = (-1/7)x + 6/7
Since the line is parallel, the slope of the new line will be the same (-1/7). Now we can substitute the x and y values of the given point (7,8) into the slope-intercept equation to find the y-intercept (b).
y = (-1/7)x + b
8 = (-1/7)(7) + b
8 = -1 + b
b = 9
Therefore, the equation of the line parallel to x + 7y = 6 and passing through (7,8) is y = (-1/7)x + 9.
2. (-4,8); 8x = 7y + 9
Again, we need to rearrange the given equation into slope-intercept form.
8x - 7y = 9
-7y = -8x + 9
y = (8/7)x - 9/7
The slope of the new line will be the same (8/7). Substituting the x and y values of the given point (-4,8) into the slope-intercept equation helps us find the y-intercept.
y = (8/7)x + b
8 = (8/7)(-4) + b
8 = -32/7 + b
b = 64/7
Therefore, the equation of the line parallel to 8x = 7y + 9 and passing through (-4,8) is y = (8/7)x + 64/7.
3. (8,9); 5x + y = 9
Rearrange the given equation into slope-intercept form.
y = -5x + 9
Since the line is parallel, the slope of the new line will be the same (-5). Substitute the x and y coordinates of the given point (8,9) to find the y-intercept.
y = -5x + b
9 = -5(8) + b
9 = -40 + b
b = 49
Hence, the equation of the line parallel to 5x + y = 9 and passing through (8,9) is y = -5x + 49.
4. (2,-6); 8x + 7y = 5
Rearrange the given equation into slope-intercept form.
7y = -8x + 5
y = (-8/7)x + 5/7
Since the line is parallel, the slope of the new line will be the same (-8/7). Use the x and y values of the given point (2,-6) to calculate the y-intercept.
y = (-8/7)x + b
-6 = (-8/7)(2) + b
-6 = -16/7 + b
b = -34/7
Therefore, the equation of the line parallel to 8x + 7y = 5 and passing through (2,-6) is y = (-8/7)x - 34/7.