Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Find the equation of the straight line that has slope m = 4
and passes through the point (–1, –6).Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = –1 and y = –6.In the slope-intercept form of a straight line, I have y, m, x, and b. So the only thing I don't have so far is a value for is b (which gives me the y-intercept). Then all I need to do is plug in what they gave me for the slope and the x and y from this particular point, and then solve for b:y = mx + b
(–6) = (4)(–1) + b
–6 = –4 + b
–2 = bThen the line equation must be "y = 4x – 2".What if they don't give you the slope?Find the equation of the line that passes through the points (–2, 4) and (1, 2).Well, if I have two points on a straight line, I can always find the slope; that's what the slope formula is for.Now I have the slope and two points. I know I can find the equation (by solving first for "b") if I have a point and the slope. So I need to pick one of the points (it doesn't matter which one), and use it to solve for b. Using the point (–2, 4), I get: ADVERTISEMENT y = mx + b
4 = (– 2/3)(–2) + b
4 = 4/3 + b
4 – 4/3 = b
12/3 – 4/3 = b
b = 8/3...so y = ( – 2/3 ) x + 8/3.On the other hand, if I use the point (1, 2), I get:y = mx + b
2 = (– 2/3)(1) + b
2 = – 2/3 + b
2 + 2/3 = b
6/3 + 2/3 = b
b = 8/3So it doesn't matter which point I choose. Either way, the answer is the same:y = (– 2/3)x + 8/3
and passes through the point (–1, –6).Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = –1 and y = –6.In the slope-intercept form of a straight line, I have y, m, x, and b. So the only thing I don't have so far is a value for is b (which gives me the y-intercept). Then all I need to do is plug in what they gave me for the slope and the x and y from this particular point, and then solve for b:y = mx + b
(–6) = (4)(–1) + b
–6 = –4 + b
–2 = bThen the line equation must be "y = 4x – 2".What if they don't give you the slope?Find the equation of the line that passes through the points (–2, 4) and (1, 2).Well, if I have two points on a straight line, I can always find the slope; that's what the slope formula is for.Now I have the slope and two points. I know I can find the equation (by solving first for "b") if I have a point and the slope. So I need to pick one of the points (it doesn't matter which one), and use it to solve for b. Using the point (–2, 4), I get: ADVERTISEMENT y = mx + b
4 = (– 2/3)(–2) + b
4 = 4/3 + b
4 – 4/3 = b
12/3 – 4/3 = b
b = 8/3...so y = ( – 2/3 ) x + 8/3.On the other hand, if I use the point (1, 2), I get:y = mx + b
2 = (– 2/3)(1) + b
2 = – 2/3 + b
2 + 2/3 = b
6/3 + 2/3 = b
b = 8/3So it doesn't matter which point I choose. Either way, the answer is the same:y = (– 2/3)x + 8/3
(2-a)x is the slope and a is the y-intercept the reason why is because the equation is already in y=mx+b form so (2-a)x is the slope and a is the y-intercept
slope=(2-a)x
y-intercept=a
slope=(2-a)x
y-intercept=a
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
