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Answer:

[tex]m=\dfrac{5}{2}[/tex]

Step-by-step explanation:

If the equation of the line is

[tex]y=mx+b,[/tex]

then m represents the slope of the line and b represents the y-intercept of the line. This equation is called the equation of the line in the slope form.

Rewrite the equation of the line in the slope form

[tex]y-4=\dfrac{5}{2}(x-2)\\ \\y-4=\dfrac{5}{2}x-\dfrac{5}{2}\cdot 2\\ \\y-4=\dfrac{5}{2}x-5\\ \\y=\dfrac{5}{2}x-1[/tex]

Thus, the slope of the line is

[tex]m=\dfrac{5}{2}[/tex]

The slope of a line whose equation is [tex]y-4 = \frac{5}{2}(x-2)[/tex] is [tex]\frac{5}{2}[/tex]

Further Explanation

Slope/gradient

  • Slope or the gradient of a line refers to the change along the y-axis divided by the change along the x-axis.
  • The slope of the line can be calculated from two co-ordinates of the line in question or obtained from the equation of a line

Equation of a straight line  

  • Equation of a straight line is written in the form [tex]y=mx+ c[/tex], where m and c are numbers.
  • m is the slope or gradient of the line while c is the y-intercept.

Equation of a straight line can be found when given:

  1. A slope of the line and one point where the line is passing through  
  2. Two points where the line is passing through
  3. A slope of the line and the y-intercept  

In this case;

The equation in question is;

[tex]y-4 = \frac{5}{2}(x-2)[/tex]

Combining like terms;

[tex]y= \frac{5}{2}x-5+4[/tex]

The equation of the line is

[tex]y= \frac{5}{2}x-1[/tex]

From the equation the slope of the line is [tex]\frac{5}{2}[/tex], while

The y-intercept is -1

Keywords: Slope, Equation of a straight line, y-intercept,  

Learn more about:  

  • Equations of a straight line: brainly.com/question/4932386
  • Slope of a straight line: brainly.com/question/4932386
  • Double intercept: brainly.com/question/4932386

Level: High school  

Subject: Mathematics  

Topic: Equation of a straight line  

Sub-topic: Slope/gradient of a line