Answer :
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
