Use the given conditions to write an equation for the line in slope-intercept form.?

Question

Passing through (4,3) and parallel to the line whose equation is y=-1/6+4.

Answer 1

Hi,

First of all, I would determine the slope. I'm assuming you meant to write the equation as: y=-1/6x+4. That being the case, the slope is next to the "x." So, the slope in this case is: -1/6. Since they asked you to write a new equation that is parallel to this line they must have the same slope which again is -1/6. According to slope-intercept form (y=mx+b), m is the slope and b is the point where the line intersects the y-axis. So we now know m=-1/6 and, in giving me a point (4,3), they have also given me an x-value and a y-value: x = 4 and y = 3. In the slope-intercept form of a straight line, I have y, m, x, and b. So the only thing I don't have a value for is b (which gives me the y-intercept). Then all I need to do is plug in my slope and the x and y from this particular point, and then solve for b:

y = mx + b
(3) = (-1/6)(4) + b
3 = –2/3 + b
so,
11/3 = b

Then the line equation passing through (4,3) and parallel to "y=-1/6x + 4", must be:

"y = -1/6x + 11/3" (answer)

Hope this helps you learn it,

SA

Answer 2

You have to plot the point (4,3) on a graph. Draw a line with slope of -1/6, and see where that crosses the Y intercept.

Then you'd get y = (-1/6)x + [insert y intercept]

Answer 3

Well i'm assuming you meant the line y= -x/6 + 4
y=-1/6+4 is a point not a line.

If this is the case:
y=-x/6+4
slope m = -1/6

slope intercept form is y = mx + b
Since we know the line is parrallel we know the slopes are the same

y = -x/6 +b

Since we know it goes through point (4,3)

3 = -4/6 + b
b = 11/3

Therefor the equation is: y = -x/6 + 11/3