How do you write the point-slope form of an equation of the line that passes through the given point (-5,7), (0, 1/2)?

Question

Genesis Allen · Accepted Answer

See a solution process below:

First, we need to determine the slope of the line. 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)(1/2) - color(blue)(7))/(color(red)(0) - color(blue)(-5)) = (color(red)(1/2) - color(blue)(7))/(color(red)(0) + color(blue)(5)) = (color(red)(1/2) - (2/2 xx color(blue)(7)))/5 = # #(color(red)(1/2) - 14/2)/5 = (-13/2)/5 = -13/10# 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. Substituting the slope we calculated and the values from the first point in the problem gives: #(y - color(red)(7)) = color(blue)(-13/10)(x - color(red)(-5))# #(y - color(red)(7)) = color(blue)(-13/10)(x + color(red)(5))# We can also substitute the slope we calculated and the values from the second point in the problem giving: #(y - color(red)(1/2)) = color(blue)(-13/10)(x - color(red)(0))# Or #(y - color(red)(1/2)) = color(blue)(-13/10)x#

Jace Anderson · Answer

undefined To write the point-slope form of an equation of the line passing through the given points (-5,7) and (0, 1/2), you first need to find the slope using the formula:

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

Substituting the coordinates of the points into the formula:

m = (1/2 - 7) / (0 - (-5))
m = (1/2 - 7) / 5
m = (-13/2) / 5
m = -13/10

Now, you can choose one of the points and use the point-slope formula:

y - y1 = m(x - x1)

Let's use the point (-5,7):

y - 7 = -13/10(x - (-5))
y - 7 = -13/10(x + 5)

This is the point-slope form of the equation of the line passing through the given points.