Question

Write the point-slope form of the equation of the line through the given points ( − 4, 1) and (4, 4)

Answer 1

The slope-point form:

$y=mx+b$

The formula of a slope:

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

We have the points (-4, 1) and (4, 4). Substitute:

$m=d\frac{4-1}{4-(-4)}=\dfrac{3}{8}$

Therefore we have the equation of a line

$y=\dfrac{3}{8}x+b$

Put the coordinates of the point (4, 4) to the euation of a line:

$4=\dfrac{3}{8}(4)+b$

$4=\dfrac{3}{2}+b$

$4=1.5+b$      subtract 1.5 from both sides

$2.5=b\to b=2.5\to b=\dfrac{5}{2}$

Answer: $\boxed{y=\dfrac{3}{8}x+\dfrac{5}{2}}$