Question

Write in slope-intercept form an equation of the line that passes through the points (−4, 2) and (6,−3).

Answer 1

Step-by-step explanation:

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Answer 2

Given:

A line that passes through the points (−4, 2) and (6,−3).

To find :

The equation in slope intercept form.

Formula to be used:

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

Equation of the line, y = mx + c

Solution:

Step 1 of 2:

The slope of the line passing through the points (−4, 2) and (6,−3) can be find using the following formula,

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

Let,

$x_1 = -4 , y_1 = 2\\x_2 = 6 ,y_2 = -3$

m = $\frac{-3-2}{6-(-4)}$

m =$\frac{-5}{10}$

m = $-\frac{1}{2}$

Therefore the slope of the line is  $-\frac{1}{2}$

Step 2 of 2:

Using the Slope and one of the points we can find the y - intercept

Let, m =  $-\frac{1}{2}$

(x , y ) = ( -4 , 2)

y = mx + c

2 =  $-\frac{1}{2}$(-4) + c

2 = 2 + c

c = 2 - 2

c = 0

The equation of the line in slope - intercept form is,

y = mx + c

y =  $-\frac{1}{2}$ x + 0

y =  $-\frac{1}{2}$ x

Therefore the equation of the line is y =  $-\frac{1}{2}$ x

Final answer:

The equation of the line that passes through the points (−4, 2) and (6,−3) in slope - intercept form is y = $-\frac{1}{2}$ x.