Find the value of y so that the line passing through the two points has the given slope?
1. (12,y), (-6,9/7), m= -1/6
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write an equation in slope-intercept form. (then graph the equation).
2. 18y+2x-9=0
3. 3x-4y=-8
y=mx+c
m= -1/6
y=-(1/6)x+c
The point (-6,9/7) must be on that line: use it to find c by plugging in x and y like
9/7=-(1/6)(-6)+c
So what's c?
So now we have the equation of the line, we need the value of the point on that line where x=12. Plug in 12 instead of x in the equation and work out what y must be.
18y+2x-9=0
we need to write as y=mx+c
18y+2x-9=0
move everything but y to the RHS:
18y=-2x+9
y=(-2/18)x+9/18
which you can simplify a bit.
You can do the other yourself the same way.
1. To find the value of y, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (12, y) and (x2, y2) = (-6, 9/7). We are given that the slope, m, is -1/6. Substituting the given points and slope into the formula, we get:
-1/6 = (9/7 - y) / (-6 - 12)
Now we can solve for y:
-1/6 = (9/7 - y) / (-18)
Multiply both sides by -18:
3 = (9/7 - y)
Multiply both sides by 7:
21 = 9 - 7y
Rearrange the equation:
7y = 9 - 21
7y = -12
Divide by 7:
y = -12 / 7
Therefore, the value of y is -12/7.
2. To write the equation in slope-intercept form (y = mx + b), we need to isolate y on one side of the equation:
18y + 2x - 9 = 0
First, move the constant term (-9) to the other side:
18y = -2x + 9
Now, divide both sides by 18 to solve for y:
y = (-2/18)x + 9/18
Simplify the fraction:
y = (-1/9)x + 1/2
So the equation in slope-intercept form is y = (-1/9)x + 1/2. To graph this equation, plot the y-intercept at (0, 1/2) and use the slope (-1/9) to find another point on the line.
3. Given the equation 3x - 4y = -8, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, subtract 3x from both sides:
-4y = -3x - 8
Next, divide both sides by -4 to solve for y:
y = (-3x - 8) / -4
Simplify the equation:
y = (3/4)x + 2
So the equation in slope-intercept form is y = (3/4)x + 2. To graph this equation, plot the y-intercept at (0, 2) and use the slope (3/4) to find another point on the line.