What is the equation of a line that is parallel to -3x+4y=4 and passes through the point (4,0)

y = 3/4x - 3

Step-by-step explanation:

If you write the equation in slope-intercept form, you will need the slope(m) and the y-intercept(b):

y = mx + b

To solve this, you first need to know the slope of the line in the given equation. In order to do this, change it to slope-intercept form for easy analyzation:

-3x + 4y = 4

= 4y = 3x + 4

= y = 3/4x + 1

Now, you know the slope(m) is 3/4, so you have this much of the slope-intercept equation:

y = 3/4x + b

At this point, you need to find the y-intercept. This can be done by plugging in the given point in the equation and solving for b:

using (4, 0) and y = 3/4x + b,

(0) = 3/4(4) + b

0 = 3 + b

b = -3

So, that means that the equation for the line is:

y = 3/4x - 3

ok then what happened.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.