How do you write an equation in point slope form given (–1, 3) and (1, 7)?

Question

Isaiah Anthony · Accepted Answer

#y-7=2(x-1)# #"the equation of a line in "color(blue)"point-slope form"# is. #•color(white)(x)y-y_1=m(x-x_1)# #"where m is the slope and "(x_1,y_1)" a point on the line"# #"to calculate m use the "color(blue)"gradient formula"# #•color(white)(x)m=(y_2-y_1)/(x_2-x_1)# #"let "(x_1,y_1)=(-1,3)" and "(x_2,y_2)=(1,7)# #rArrm=(7-3)/(1-(-1))=4/2=2# #"use either of the 2 given points as a point on the line"# #"using "(x_1,y_1)=(1,7)" then"# #rArry-7=2(x-1)larrcolor(red)"in point-slope form"#

Eli Assouline · Answer

I don't know what " point slope form" is but here's the equation
#y=2x+5# If we have two points (-1,3) and (1,7) we can find the gradient (slope). We do this by finding the difference between the two #y# values and divide this by the difference between the two #x# values 7-3=4 this is the difference in the #y# values 1--1=1+1=2 #=># difference in #x# values Gradient #=4/2# =2 The equation of the line is #y=2x+c# where the c value is the #y# intercept.( the place it crosses the #y# axis) Substitute (1,7) into the equation to find c 7=#2xx1#+c 7=2+c 5=c Put this into the equation in place of c

Eli Assouline · Answer

undefined To write an equation in point-slope form given two points, you first find the slope using the formula:

$$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

Then, you choose one of the points and the slope to plug into the point-slope form equation:

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

For the given points $(-1, 3)$ and $(1, 7)$, the slope $m$ is:

$$ m = \frac{{7 - 3}}{{1 - (-1)}} = \frac{4}{2} = 2 $$

Choosing the point $(-1, 3)$ and substituting $x_1 = -1$, $y_1 = 3$, and $m = 2$ into the point-slope form equation, we get:

$$ y - 3 = 2(x - (-1)) $$

Simplify:

$$ y - 3 = 2(x + 1) $$

$$ y - 3 = 2x + 2 $$

$$ y = 2x + 5 $$

Therefore, the equation in point-slope form is $y = 2x + 5$.