Question

Find an equation for the line satisfying the given conditions.
Through (5, 4) and parallel to 4x - 3y = 7.

Answer 1

Whenever you see parallel right away you know it has the same slope

Answer 2

first solve for this by rewriting the equation in slope intercept form

Answer 3

once you have the slope, plug in the point to y=mx+b and solve for b. This will give you the equation!!

Answer 4

4x - 3y = 7
Do the algebra to solve for y:
y = (4/3)x - (7/3) --> y = mx +b form of a linear equation where m is the slope and b is the y-intercept.
The slope of the line is (4/3).
The question now becomes the following: What is the equation of the line with slope (4/3) and passing through the point (5,4)
Use. the point-slope form of a linear equation, (y - y1) = m(x - x1) where (x1,y1) is a point on the line and m is the slope of the line.
y -4 = (4/3) (x - 5)
Solving for y to get the equation in slope-intercept form,
y = (4/3) x - (8/3) --> Check the work. Thanks.
@orbie

Answer 5

It's right but how did you get -(8/3)? @Directrix

Answer 6

@orbie --> Did you understand how I got this: y -4 = (4/3) (x - 5) ?

Answer 7

@Directrix yes

Answer 8

y -4 = (4/3) (x - 5)
y - 4 = (4/3)x + (4/3)(-5)
y - 4 = (4/3)x - 20/3
y = (4/3)x - 20/3 + 4
y = (4/3)x - 20/3 + 12/3
y = (4/3)x - (8/3)

Answer 9

ooh okay thank you!