Question

Write the​ point-slope form of the​ line's equation satisfying the given conditions. Then use the​ point-slope form of the equation to write the​ slope-intercept form of the equation. passing through (4,8) and (5,10)

Answer 1

Point slope form:
equation of a line passing through the point (x1,y1) and having a slope of m is
y-y1=m(x-x1)

y=mx+b is slope-intercept form
m=slope
b=yintercept

the slope of the line passing through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)


so

first find slope, then point slope then solve for y to get slope intercept
ok

slope
given (4,8) and (5,10), the slope is (10-8)/(5-4)=2/1=2
and a point is (4,8), or it could be (5,10)
so 2 possible point slope forms are
y-8=2(x-4) and y-10=2(x-5)
solving for y (distribute and add 8 or 10 to both sides)
y=2x+0 or
y=2x is the slope-intercept form


point-slope forms:
y-8=2(x-4) and y-10=2(x-5)

slope intercept form:
y=2x+0 or y=2x (same thing, the first one includes the intercept)

Answer 2

M= y2-y1/x2-x1 so m=10-8/5-4 which equals 2/1=2. The slope is 2.
Slope-intercept form is y=mx+b
y=2x+0