Question

What is the equation of the line in slope-intercept form?

Answer 1

Answer:

The equation of the line in slope-intercept form is:

y = x + 4

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

• m is the slope

• b is the y-intercept

Given the points on the line graph

• (0, 4)

• (1, 5)

Determining the slope between (0, 4) and (1, 5)

(x₁, y₁) = (0, 4)

(x₂, y₂) = (1, 5)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                =  [5 - 4] / [1 - 0]

                = 1 / 1  

               = 1

Thus, the slope of the line = m = 1

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 4

Thus, the y-intercept b = 4

now substituting b = 4 and m = 1 in the slope-intercept form

y = mx + b

y = (1)x + 4

y = x + 4

Therefore, the the equation of the line in slope-intercept form is:

y = x + 4