Question

What is the slope of the line whose equation is y−4=5/2(x−2)?

Answer 1

Answer:

$m=\dfrac{5}{2}$

Step-by-step explanation:

If the equation of the line is

$y=mx+b,$

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

$y-4=\dfrac{5}{2}(x-2)\\ \\y-4=\dfrac{5}{2}x-\dfrac{5}{2}\cdot 2\\ \\y-4=\dfrac{5}{2}x-5\\ \\y=\dfrac{5}{2}x-1$

Thus, the slope of the line is

$m=\dfrac{5}{2}$

Answer 2

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

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 $y=mx+ c$, 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;

$y-4 = \frac{5}{2}(x-2)$

Combining like terms;

$y= \frac{5}{2}x-5+4$

The equation of the line is

$y= \frac{5}{2}x-1$

From the equation the slope of the line is $\frac{5}{2}$, 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