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).
Point-slope form:
(y-y1)=m(x-x1)
Slope intercept form:
y=mx+b
b is the y-intercept, and m is the slope.
In the given case, m can be evalauated from the given parellel line by transforming it to slope intercept form:
3x-4y=12
y=(3/4)x - 3
so m=(3/4)
Point-slope form:
(x1,y1) = (8,3)
substitute (x1,y1) and m in the point slope form equation and voilà !
Expand the point slope form of the equation and normalize the coefficient of y to 1 to get the slope-intercept form of the equation.
Substitute (8,3) in both equations to make sure that each balances, i.e. the line passes through the given point.
To find the equation of a line parallel to a given line and passing through a given point, we can follow these steps:
Step 1 - Convert the given equation to slope-intercept form (y = mx + b).
Step 2 - Identify the slope of the given line.
Step 3 - Use the identified slope and the given point to write the equation in point-slope form.
Step 4 - Convert the equation from point-slope form to slope-intercept form.
Let's go through each step:
Step 1:
The given equation is 3x - 4y = 12.
To convert it to slope-intercept form, we isolate y:
-4y = -3x + 12
Divide every term by -4:
y = (3/4)x - 3
So, the given equation in slope-intercept form is y = (3/4)x - 3.
Step 2:
From the given equation, we can see that the slope is (3/4). This is the slope of the original line, which means the parallel line will have the same slope.
Step 3:
We can use the point-slope form equation:
y - y1 = m(x - x1)
Using the given point (8,3), we have:
y - 3 = (3/4)(x - 8)
Step 4:
To convert the equation from point-slope form to slope-intercept form, we need to isolate y on one side of the equation.
y - 3 = (3/4)(x - 8)
Distribute (3/4) on the right side:
y - 3 = (3/4)x - 6
Add 3 to both sides:
y = (3/4)x - 6 + 3
Simplify:
y = (3/4)x - 3
So, the equation of the line parallel to 3x - 4y = 12 and passing through (8,3) is:
y = (3/4)x - 3 (in both point-slope and slope-intercept forms).