Question

How do you find an equation for the line satisfying the given conditions.
Through (3, 3) and parallel to 3x - 4y = 7 ??

Answer 1

write the equation of the line in point slope form y = mx + b

or y = 3/4 x - 7/4

parallel lines have the same gradient... so use the gradient of this line and the point slope formula.. with the given point

Answer 2

Let the equation of the line be y=mx+c
m=3/4
Applying the given point and m
3=3/4*3+c
c=3/4
the eqn is y=3/4x+3/4

Answer 3

First isolate y:
-4y=-3x+7
y=(3/4)x-7/4
The slope is 3/4.
Our parallel line will have this slope as well.

Point-slope form:
\[y-y1=m(x-x1)\]
\[y-3=\frac{3}{4}(x-3)\]
slope-intercept form:
\[y=mx+b\]
\[y=\frac{3}{4}x+\frac{3}{4}\]