Question

The points (2, r) and (6, -4) lie on a line with slope 4. Find the missing coordinate r R=

Answer 1

$\text{The slope-intercept form:}\ y=mx+b\\\\\text{We have:}\ m=4\\\\\text{then}\ y=4x+b\\\\\text{The line passes through point (6; -4). Substitute:}\\\\(6;-4)\to x=6;\ y=-4\\\\-4=4\cdot6+b\\-4=24+b\ \ \ |-24\\b=-28\\\\\text{therefore:}\ y=4x-28$
$\text{substitute}\ (2;\ r)\to x=2;\ y=r\\\\r=4\cdot2-28=8-28=-20$

Answer: r = -20