Respuesta :

Louli
Answer:
y = 5x - 7

Explanation:
The general form of the linear line in slope-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept

1- getting the slope:
The slope of the line can be calculated using the following formula:
m = [tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

We are given the points:
(3,8) representing (x₁,y₁)
(2,3) representing (x₂,y₂)
Substitute with the givens in the above equation to get the slope as follows:
m = [tex] \frac{3-8}{2-3} [/tex] = 5

Therefore, the equation now became:
y = 5x + c

2- getting the y-intercept:
To get the value of the c, we will use any of the given points, substitute in the equation we got in part 1 and solve for c. I will use point (2,3) as follows:
y = 5x + c
3 = 5(2) + c
3 = 10 + c
c = 3 - 10
c = -7

Based on the above, the equation of the line is:
y = 5x - 7

Hope this helps :)

Answer:

[tex]y= 5x-7[/tex]

Step-by-step explanation:

Using slope-intercept form:

The equation of line is given by:

[tex]y=mx+b[/tex]                    .....[1]

where,

m is the slope of the line

b is the y-intercept.

As per the statement:

The points (3, 8) and (2, 3) fall on a particular line.

Using slope(m) formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points we have;

[tex]m = \frac{3-8}{2-3}=\frac{-5}{-1}=5[/tex]

⇒m = 5

Put m = 5 in [1] we have;

[tex]y=5x+b[/tex]

Substitute the point (3, 8) we have;

8 = 5(3)+b

8 = 15+b

Subtract 15 from both sides we have;

[tex]-7 = b[/tex]

or

b = -7

Then we have;

[tex]y= 5x-7[/tex]

Therefore, the equation of line in slope intercept form is, [tex]y= 5x-7[/tex]