Write an equation of a line parallel to y=3X-5 and passing through (3,2).

In order to write the equation of any line, we must know the slope of the line and a point on the line, or we must know two points on the line. In this case, the point is clearly (3,2). We can find the slope of the line from the given information. Two parallel lines must have the same slope. Using the fact that the given line is in slope-intercept form (y=mx+b), we can see that the slope is 3.

We now know a point (3,2) and the slope, which is 3. Let's use the point-slope form of line which is (y-y1)=m(x-x1) and let m=3 and (x1,y1)=(3,2). Making the substitutions, we will get (y-2)=3(x-3).

The above is the equation of the line in point-slope form. If we need to find the equation in slope-intercept form, we solve for x. First, distribute the 3 into the (x-3).
We now have y-2=3x-9, and we have to solve for y by adding 2 to both sides. This gives us the final answer of y=3x-7.

Given: By writing an equation line which is parallel to the given line y=3x-5 and passing through ( 3,2) ,
Method: For this firstly we have to write the slope of the given line by
comparing with y=mx+c, where m is the slope of line
Formula: here we used the formula of line in point- slope form
y-y1=m(x-x1) where ( x1,y1) is the point and m is the slope.
Calculation:
by comparison, we find the slope of the line as m=3 and point is given as (3,2)
Now by using the formula of line in point slope form and by putting the value of m and point which are given ,
the equation of line is
y-2=3(x-3)
on simplifying
y=3x-9+2 i.e y=3x-7
Answer: y=3x-7
Conclusion: The equation of line parallel to the given line y=3x-5 and passing through (3,2) is y=3x-7.

I can explain how to work this problem. This linear equation is written in slope-intercept form. The equation of a line in slope-intercept form is y=mx+b. The "m" in this scenario is the slope, which is the rate of change. The "b" in the problem is the y-intercept. The y-intercept is the point at which the line crosses the y-axis.
To work this problem, you have to also know that all parallel lines have the same slope. This means that the slope of your new equation here will also be three.
To solve, plug in your values for x and y. In the ordered pair (3,2), 3 is the x-coordinate and 2 is the y-coordinate. When these values are plugged in, the equation looks like this:
(2)=3(3)-b. Parallel lines do not have the same y-intercept, so you are looking for a new value of "b."
2=9-b. Subtract 9 from both sides of the equation and you get this:
-7=-b. Divide by negative one on both sides in order to make b positive.
b=7. The parallel line to y=3x-5 that passes through (3,2) is y=3x+7.