Find the Linear Function with Slope 6y Through Point (6,41)

Question

A straight line has a slope of 6y and passes through the points $(6,41)$ .

Which function corresponds to the line described?

Video Solution

Solution Steps

00:00 Find the algebraic representation for the function

00:03 We'll use the straight line equation

00:09 We'll substitute the point according to the given data

00:13 We'll substitute the line's slope according to the given data

00:21 We'll continue solving to find the intersection point

00:29 We'll isolate intersection point B

00:37 This is the intersection point with the Y-axis

00:46 Now we'll substitute the intersection point and slope in the line equation

00:54 We'll factor 6 into 2 and 3

01:06 We'll factor 5 into 2 and 2.5

01:14 We'll factor out the common term from the parentheses

01:21 And this is the solution to the question

Step-by-Step Solution

To solve the exercise, we will start by inserting the available data into the equation of the line:
y = mx + b
41 = 6*6 + b
41 = 36 +b
41-36 = b
5 = b

Now we have the data for the equation of the straight line:

y = 6x + 5
But it still does not match any of the given options.

Keep in mind that a common factor can be excluded:
y = 2(3x + 2.5)

Answer

$y=2(3x+2\frac{1}{2})$

Related Subjects

Graphs of Direct Proportionality Functions

Question Types

Graphical Representation: Determining the slope of a function with a point