Find the equation of the line that passes through (2, 4) and is parallel to the line y = 3x – 8.

y=3x-2

Step-by-step explanation:

y=3x-2

Step-by-step explanation:

To find an equation that is parallel to the given line, we know that the slope will be the same. The slope MUST be the same because if the slope is different, the lines will touch at one point. Parallel lines NEVER touch or cross, therefore, the slope is the same.

y=3x+b

To figure out the line, we use the given point and plug that into x and y.

4=3(2)+b                    [multiply]

4=6+b                         [subtract both sides by 6]

b=-2

Now that we know the y-intercept, we can complete the equation.

y=3x-2

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.