given the line 5x-4y=8, find the equation of a line parallel to this line that passes through the point (3, -2)

thank you

also part B

find the equation of a line perpendicular to this line that passes through the point (3, -2)

thanks

looks like you need to review slopes

parallel lines have equal slopes
perpendicular lines with slopes m1 and m2 have m1 * m2 = -1

(A) 5x-4y=8 has slope 5/4
Now you have a point and a slope, so use the point-slope form of the line
y+2 = 5/4 (x-3)

(B) the perpendicular line has slope -4/5
y+2 = -4/5 (x-3)

rearrange as you like.

Or, just modify the equation they gave you. You want a parallel line, so
5x-4y=C
it passes through (3,-2), so
5(3) - 4(-2) = C
will do the job.

to get the line perpendicular to 5x-4y=8 use
4x+5y=C
4(3) + 5(-2) = C

To find the equation of a line parallel to the given line and passing through the point (3, -2), follow these steps:

Step 1: Determine the slope of the given line.
The given equation is in the form Ax + By = C, where A = 5, B = -4, and C = 8. To find the slope, we need to rearrange the equation in the form y = mx + b, where m is the slope. Doing so:

5x - 4y = 8
-4y = -5x + 8
y = (5/4)x - 2

So, the slope of the given line is 5/4.

Step 2: Since the line we're looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also 5/4.

Step 3: Use the slope-intercept form of the line (y = mx + b) and substitute the coordinates (3, -2) to find the value of b (the y-intercept).

-2 = (5/4)(3) + b
-2 = (15/4) + b
Multiply every term by 4 to eliminate fractions:
-8 = 15 + 4b
-23 = 4b
b = -23/4

Step 4: The equation of the line parallel to the given line and passing through the point (3, -2) is:
y = (5/4)x - 23/4

Therefore, the equation of the line parallel to the given line that passes through the point (3, -2) is y = (5/4)x - 23/4.

To find the equation of a line parallel to the given line, we need to find its slope first. The given line is in the form Ax + By = C, where 5x - 4y = 8.

To find the slope, we rearrange the equation to the slope-intercept form (y = mx + b), where m is the slope:

5x - 4y = 8
-4y = -5x + 8
y = (5/4)x - 2

From this equation, we can determine that the slope of the given line is 5/4.

Since we want to find a line parallel to this line, the parallel line will have the same slope.

Now, we can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find the equation of the parallel line, where (x₁, y₁) represents the given point (3, -2) and m represents the slope (5/4):

y - (-2) = (5/4)(x - 3)
y + 2 = (5/4)x - (15/4)

To simplify this equation, we multiply both sides by 4 to eliminate fractions:

4y + 8 = 5x - 15

Finally, we rearrange the equation to the standard form (Ax + By = C):

5x - 4y = 23

So, the equation of the line parallel to the given line and passing through the point (3, -2) is 5x - 4y = 23.