# Find the equation of the line between points (5,4) and (-3,-2).   Put your final answer in y = mx + b form, and give fractions in simplest form.

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should first find the point slope form of equation of line passing through the given points, `y - y_0 = m(x - x_0)` , and then you need to convert the point slope form into the slope intercept form, `y = mx + b.`

Considering the point having the coordinates `x_0 = -3, y_0 = -2, ` yields:

`y + 2 = m(x + 3)`

You need to evaluate the slope `m` , using the following formula:

`m = (y_1 - y_0)/(x_1 - x_0)`

Considering `x_1 = 5, y_1 = 4` , yields:

`m = (4 + 2)/(5 + 3) => m = 6/8 => m = 3/4`

Replacing 3/4 for m in point slope form of equation of line, yields:

`y + 2 = (3/4)(x + 3)`

You need to convert the point slope form of equation of line into the slope intercept form, hence, you need to isolate y to the left side, such that:

`y = (3/4)(x + 3) - 2`

`y = (3/4)x + 9/4 - 2`

`y = (3/4)x + (9 - 8)/4 => y = (3/4)x + 1/4 => {(m = 3/4),(b = 1/4):}`

Hence, evaluating the equation of the line passing through the given points, in slope intercept form, yields `y = (3/4)x + 1/4.`