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Find the equation (in terms of x ) of the line through the points (-4,-2) and (3,3)

User Alextoni
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Sure, let's find the equation of the line passing through the points (-4,-2) and (3,3). The equation of a line in the slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.

First, we calculate the slope (m) of the line. This can be done using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1,y1) and (x2,y2) are the coordinates of the two given points. Substituting the given points (-4,-2) as (x1,y1) and (3,3) as (x2,y2), the equation becomes:

m = (3 - (-2)) / (3 - (-4)) = 0.7142857142857143

So, the slope of the line m is approximately 0.714.

Next, we find the y-intercept (b) of the line. Using one of the points on the line (let's use (-4,-2) as (x1,y1)) and the slope, we can use the equation:

b = y1 - m*x1

Substituting the values, we get:

b = -2 - 0.714*(-4) = 0.8571428571428572

So, the y-intercept of the line b is approximately 0.857.

Hence, the equation of the line passing through (-4, -2) and (3, 3) is:

y = 0.714x + 0.857 which is approximately equal to y = 0.7142857142857143x + 0.8571428571428572.

User Guzman Ojero
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