Question

Write the equation of the line in the form Y = MX where M is the slope.

Answer 1

Answer:

We conclude that the equation of the line in the form $y = mx + b$ will be:  $y=\frac{1}{2}x$

Step-by-step explanation:

From the given graph, taking two points

• (0, 0)

• (10, 5)

Important Tip:

The slope-intercept form of the line equation

$y = mx+b$

where

• $m$ represents the slope

• $b$ represents the y-intercept

1 of 3 steps:

Determine the slope

We need to find the slope of the line containing the points (0, 0) and (10, 5)

$m=\frac{y_2-y_1}{x_2-x_1}$

where $m$ is the slope between (x₁, y₁) and (x₂, y₂)

In our case,

• (x₁, y₁) = (0, 0)  

• (x₂, y₂) = (10, 5)

substituting (x₁, y₁) = (0, 0) and (x₂, y₂) = (10, 5) in the slope formula

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{5-0}{10-0}$

Refine

$m=\frac{1}{2}$

Thus, the slope of the line containing the points (0, 0) and (10, 5) is: $m=\frac{1}{2}$

2 of 3 steps:

Determine the y-intercept

We can determine the y-intercept by determining the value of y at x = 0.

From the graph, it is clear that at x = 0 the value of y = 0.

Thus, the y-intercept of the line is: $b = 0$

3 of 3 steps:

Substitute the values in the slope-intercept form

Substitute the values $m=\frac{1}{2}$ and $b = 0$ in the slope-intercept form

$y = mx+b$

$y\:=\:\frac{1}{2}x+0$

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

Conclusion:

Therefore, we conclude that the equation of the line in the form $y = mx + b$ will be:  $y=\frac{1}{2}x$