Question
Write the equation of the line that contains the points (3,7) (-3,-3)
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Answer to a math question Write the equation of the line that contains the points (3,7) (-3,-3)
Santino
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To write the equation of the line that passes through the points \( (3,7) \) and \( (-3,-3) \) , we need to find the slope (m) of the line using the formula:
m = \frac{y_2 - y_1}{x_2 - x_1}
Substituting the given points into the formula:
m = \frac{-3 - 7}{-3 - 3} = \frac{-10}{-6} = \frac{5}{3}
Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
y - y_1 = m(x - x_1)
Using the point \( (3,7) \) and the slope \( \frac{5}{3} \) , the equation becomes:
y - 7 = \frac{5}{3}(x - 3)
To write this in slope-intercept form (\( y = mx + b \)) , we distribute the slope and simplify:
y - 7 = \frac{5}{3}x - 5
y = \frac{5}{3}x + 2
Therefore, the equation of the line that contains the points \( (3,7) \) and \( (-3,-3) \) is **\( y = \frac{5}{3}x + 2 \) **.
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