How do you write an equation of a line with points (-5,3), (0,-7)?

Question

Genesis Allen · Accepted Answer

#(y - color(red)(3)) = color(blue)(-2)(x + color(red)(5))#

or

#(y + color(red)(7)) = color(blue)(-2)x#

Or

#y = color(blue)(-2)x - 7# We can use the point-slope formula to write an equation. However, we must first determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line. Substituting the values from the points in the problem gives: #m = (color(red)(-7) - color(blue)(3))/(color(red)(0) - color(blue)(-5))# #m = (color(red)(-7) - color(blue)(3))/(color(red)(0) + color(blue)(5)) = -10/5 = -2# The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))# Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through. We can substitute the slope we calculated and the first point giving: #(y - color(red)(3)) = color(blue)(-2)(x - color(red)(-5))# #(y - color(red)(3)) = color(blue)(-2)(x + color(red)(5))# We can also substitute the slope we calculated and the second point giving: #(y - color(red)(-7)) = color(blue)(-2)(x - color(red)(0))# #(y + color(red)(7)) = color(blue)(-2)x# Or, we can solve this equation for #y# to give an equation in slope-intercept form: #y + color(red)(7) = color(blue)(-2)x# #y + color(red)(7) - 7 = color(blue)(-2)x - 7# #y + 0 = color(blue)(-2)x - 7# #y = color(blue)(-2)x - 7#

Eva Adamson · Answer

undefined To write the equation of a line given two points, you can use the point-slope form of the equation, which is:

$$ y - y_1 = m(x - x_1) $$

where $ m $ is the slope of the line, and $ (x_1, y_1) $ is one of the given points.

Given the points (-5, 3) and (0, -7), we can first find the slope:

$$ m = \dfrac{y_2 - y_1}{x_2 - x_1} $$
$$ m = \dfrac{-7 - 3}{0 - (-5)} $$
$$ m = \dfrac{-10}{5} $$
$$ m = -2 $$

Now, using the point-slope form with the point (-5, 3):

$$ y - 3 = -2(x - (-5)) $$
$$ y - 3 = -2(x + 5) $$
$$ y - 3 = -2x - 10 $$
$$ y = -2x - 10 + 3 $$
$$ y = -2x - 7 $$

So, the equation of the line passing through the points (-5, 3) and (0, -7) is $ y = -2x - 7 $.