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:

$\:y=-\frac{1}{6}x\:+\:4$

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)

• (3, 3.5)

Determining the slope between (0, 4) and (3, 3.5)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{3.5-4}{3-0}$

$m=\frac{\frac{7}{2}-4}{3-0}$

$m=-\frac{1}{6}$

Thus, the slope of the line = m = -1/6

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 = -1/6 in the slope-intercept form

$y = mx + b$

$\:y=-\frac{1}{6}x\:+\:4$

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

$\:y=-\frac{1}{6}x\:+\:4$