What is the equation of the line, in slope-intercept form, that passes through (4, 2) and (-2, -3)?

Solution:

The formula to find the slope of two points (x₁, y₁) and (x₂, y₂) is

m = (y₂ - y₁) / (x₂ - x₁)

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

m = (-3 - 2) / (-2 - 4)

m = -5/ -6

m = 5/6

Now using the slope and the point (4, 2) the y intercept is

y = mx + b

2 = 5/6 (4) + b

2 = 10/3 + b

By further calculation,

b = 2 - 10/3

Taking LCM

b = (6 - 10)/3 = -4/3

By writing the equation in slope intercept form

y = mx + b

y = 5/6x - 4/3

Therefore, the equation of the line in slope intercept form is y = 5/6 x - 4/3.

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What is the equation of the line, in slope-intercept form, that passes through (4, 2) and (-2, -3)?

Summary:

The equation of the line, in slope-intercept form, that passes through (4, 2) and (-2, -3) is y = ⅚ x - 4/3.