How do you write an equation in point-slope form for the given (–2, 1) and (4, 13)?

Question

Isaiah Anthony · Accepted Answer

Use the slope formula to find slope #m = 2#, then use the second point to get:

#y - 13 = 2(x - 4)# Given two points #(x_1, y_1)# and #(x_2, y_2)#, then the slope #m# of a line through those two points is given by the formula: #m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1)# In our case, let #(x_1, y_1) = (-2, 1)# and #(x_2, y_2) = (4, 13)#. Then: #m = (13 - 1) / (4 - (-2)) = 12 / 6 = 2# Then point slope form for a line is: #y - y_0 = m(x - x_0)# where #m# is the slope and #(x_0, y_0)# is some point on the line. To avoid double minus signs, let's use the second point #(4, 13)# to get: #y - 13 = 2(x-4)#

Savannah Anderson · Answer

undefined To write an equation in point-slope form for the given points $(-2, 1)$ and $(4, 13)$, you would first find the slope using the formula $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points. Then, you would use one of the points and the slope in the point-slope form equation $y - y_1 = m(x - x_1)$.

1. Calculate the slope: $m = \frac{{13 - 1}}{{4 - (-2)}} = \frac{{12}}{{6}} = 2$
2. Choose one of the points, for example $(-2, 1)$, and substitute into the point-slope form equation: $y - 1 = 2(x - (-2))$ 
3. Simplify: $y - 1 = 2(x + 2)$
4. Distribute: $y - 1 = 2x + 4$
5. Add 1 to both sides: $y = 2x + 5$

So, the equation in point-slope form for the given points is $y = 2x + 5$.