What is the equation of the line that passes through the given pair points in slope-intercept form?
a. (2, 5.1) and (−1, −0.5)
b. (−2, 3) and (3, −4)

a. The equation of the line is

b. The equation of the line is

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

y = mx + c

where m is the slope and c is the y-intercept

1. To get the slope:

where (x₁ , y₁) and (x₂ , y₂) are two points that belong to the line

2. To get the y-intercept:

We pick any point (x , y) that belong to the line and use this point to substitute in the general equation:

y = mx + c

m is calculated from part 1 and (x , y) is a known point on the line. So, we solve for c which is the only unknown.

Now, for the required lines:

Part a:

The two given points are (2, 5.1) and (-1, -0.5)

representing (x₁ , y₁) and (x₂ , y₂)

i. Getting the slope:

ii. Getting the y-intercept:

I will use the point (-1, -0.5)

y = mx + c

iii. Based on the above calculations, the equation of the line is:

Part b:

The two given points are (-2, 3) and (3, -4)

representing (x₁ , y₁) and (x₂ , y₂)

i. Getting the slope:

ii. Getting the y-intercept:

I will use the point (3, -4)

y = mx + c

iii. Based on the above calculations, the equation of the line is:

Hope this helps :)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0