Find the distance between each pair of parallel lines

y= -3/4x-1
3x+4y=20

Please help

well, graph the lines

or find some points from them and then measure the distance through adding/ subtraction

Let me first convert them into the same y = mx + b form:

-->y = -(3/4)x - 1
-->y = -(3/4)x + 5

Okay, slopes are the same so you know they're parallel to each other. Looking at the y-intercept you know that one has a coordinate of (0,-1) and the other has a coordinate of (0,5).

Now knowing that information, you should be able to calculate the distance with the distance formula. If you still stuck, let me know.

sorry but that was no help to me

To find the distance between two parallel lines, you can use the formula which involves the coefficients of the variables (x and y) in the equations of the lines.

In your case, the equations of the parallel lines are:

y = -3/4x - 1 -------- (1)
3x + 4y = 20 -------- (2)

First, we need to rewrite the equation (2) in the slope-intercept form (y = mx + c), where m is the slope and c is the y-intercept. Rearranging equation (2), we get:

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

Comparing equations (1) and (2), we can see that the slopes of both lines are the same, and since the slopes of parallel lines are equal, this confirms that the given lines are indeed parallel.

Now, to find the distance between the parallel lines, let's consider a point on one line and calculate the perpendicular distance from that point to the other line:

We can take any convenient point on one of the lines, such as the point (0, -1) from equation (1). Now, we can substitute this point into the equation (2) to find the perpendicular distance. The perpendicular distance (d) is given by the formula:

d = |Ax + By + C| / sqrt(A^2 + B^2)

where A, B, and C are the coefficients of x, y, and the constant term in the equation of the line we want to measure the distance to.

Substituting the values A = 3, B = 4, and C = -20 into the formula, we get:

d = |(3*0) + (4*(-1)) + (-20)| / sqrt(3^2 + 4^2)
= |-4 - 20| / sqrt(9 + 16)
= |-24| / sqrt(25)
= 24 / 5
= 4.8 units

Therefore, the distance between the given pair of parallel lines is 4.8 units.