Write the equation for a line in point slope form and in slope intercept form parallel to 3x-4y=12 and passes through (8,3).

well, the slope is 3/4

so plug that into the other forms.

y = 3/4 x + ?

y-k = 3/4 (x-h)

y = (3/4) x - 3

so slope = 3/4

y = (3/4) x + b
3 = (3/4)8 + b
b = -3
so
y = (3/4) x - 3

or
3/4 = (y-3)/(x-8)

To find the equation of a line parallel to the line 3x - 4y = 12 and passing through the point (8,3), we need to use the concept of parallel lines having the same slope.

1) Equation in point-slope form:
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1),
where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope of the line 3x - 4y = 12, we need to rearrange the equation in the slope-intercept form y = mx + b, where m represents the slope. Therefore, we proceed as follows:

3x - 4y = 12
-4y = -3x + 12
y = (3/4)x - 3

As we can see, the slope of the line is 3/4.

Now, we can use the point-slope form with the given point (8,3) and the slope 3/4 to find the equation of the parallel line:

y - 3 = (3/4)(x - 8)

This equation in point-slope form is for a line parallel to 3x - 4y = 12 and passing through the point (8,3).

2) Equation in slope-intercept form:
The slope-intercept form of a linear equation is given by:
y = mx + b,
where m is the slope of the line, and b is the y-intercept.

Using the point-slope form equation found earlier, we can convert it into slope-intercept form:

y - 3 = (3/4)(x - 8)
y - 3 = (3/4)x - 3(3/4)
y - 3 = (3/4)x - 9/4
y = (3/4)x + (9/4) - (12/4)
y = (3/4)x - (3/4)

This equation in slope-intercept form represents the line parallel to 3x - 4y = 12 and passing through the point (8,3).