Question 579606
Write the equation of the line containing the points (-2,5) and (6,1).
:
a. Find the slope between the two points in simplest form
Use the slope formula: m = {{{(y2-y1)/(x2-x1)}}}
Assign the given points as follows
x1=-2; y1=5
x2=6; y2 =1
:
m = {{{(1-5)/(6-(-2))}}} = {{{(-4)/8}}} = {{{-1/2}}} is the slope
Use the point/slope form to write the equation
y - y1 = m(x - x1)
y - 5 = {{{-1/2}}}(x - (-2))
y - 5 = {{{-1/2}}}(x + 2)
y - 5 = {{{-1/2}}}x - 1
y = {{{-1/2}}}x - 1 + 5
y = {{{-1/2}}}x + 4, is the equation
;
:
b. Substitute the slope into the equation along with one of the points listed above and solve the y-intercept
we already did that, the y intercept occurs when x=0, therefore
y = {{{-1/2}}}(0) + 4
y = 0 + 4
y = 4 is the y intercept

c. Rewrite the equation of the line with the slope and y-intercept
y = {{{-1/2}}}x + 4