To ascertain if a point is on a line we must plug that coordinate pair into the equation of the line. If a true statement such as 5=5 is returned then we know that point is on our line. 

\(\displaystyle y=6x-5\)

Choose the point you suspect is on the line.

\(\displaystyle (2,7)\)

\(\displaystyle 7=6(2)-5\)

\(\displaystyle 7=7\)

Since the equation returned a true statement the point \(\displaystyle \mathbf{(2,7)}\) is on our line.

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=16\) into the given equation will give the following:

\(\displaystyle y=-2x+12\)

\(\displaystyle y=-2(16)+12=-32+12=-20\)

Thus, \(\displaystyle (16, -20)\) is on the line.

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=24\) into the given equation will give the following:

\(\displaystyle y=\frac{1}{6}x+5\)

\(\displaystyle y=\frac{1}{6}(24)+5=4+5=9\)

Thus, \(\displaystyle (24, 9)\) is on the line.

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=10\) into the given equation will give the following:

\(\displaystyle y=-10x+8\)

\(\displaystyle y=-10(10)+8=-100+8=-92\)

Thus, \(\displaystyle (10, -92)\) is on the line.

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=1\) into the given equation will give the following:

\(\displaystyle y=13x-11\)

\(\displaystyle y=13(1)-11=13-11=2\)

Thus, \(\displaystyle (1, 2)\) is on the line.

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=-10\) into the given equation will give the following:

\(\displaystyle y=-\frac{3}{2}x+10\)

\(\displaystyle y=-\frac{3}{2}(-10)+10=15+10=25\)

Thus, \(\displaystyle (-10, 25)\) is on the line.

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=-20\) into the given equation will give the following:

\(\displaystyle y=\frac{1}{5}x-5\)

\(\displaystyle y=\frac{1}{5}(-20)-5=-4-5=-9\)

Thus, \(\displaystyle (-20, -9)\) is on the line.

Start by rewriting the equation into slope-intercept form.

\(\displaystyle 3x+4y=5\)

\(\displaystyle 4y=-3x+5\)

\(\displaystyle y=-\frac{3}{4}x+\frac{5}{4}\)

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=12\) into the given equation will give the following:

\(\displaystyle y=-\frac{3}{4}x+\frac{5}{4}\)

\(\displaystyle y=-\frac{3}{4}(12)+\frac{5}{4}=-9+\frac{5}{4}=-\frac{31}{4}\)

Thus, \(\displaystyle (12, -\frac{31}{4})\) is on the line.

Start by rewriting the equation into slope-intercept form.

\(\displaystyle 12x-4y=18\)

\(\displaystyle -4y=-12x+18\)

\(\displaystyle y=3x-\frac{9}{2}\)

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=-13\) into the given equation will give the following:

\(\displaystyle y=3x-\frac{9}{2}\)

\(\displaystyle y=3(-13)-\frac{9}{2}=-39-\frac{9}{2}=-\frac{87}{2}\)

Thus, \(\displaystyle (-13, -\frac{87}{2})\) is on the line.

Start by rewriting the equation into slope-intercept form.

\(\displaystyle 5y+10x=20\)

\(\displaystyle 5y=-10x+20\)

\(\displaystyle y=-2x+4\)

To find which point is on the line, take the \(\displaystyle x\)-coordinate, and plug it into the given equation to solve for \(\displaystyle y\). If the \(\displaystyle y\)-value matches the \(\displaystyle y\)-coordinate of the same point, then the point is on the line.

Plugging in \(\displaystyle x=-7\) into the given equation will give the following:

\(\displaystyle y=-2x+4\)

\(\displaystyle y=-2(-7)+4=18\)

Thus, \(\displaystyle (-7, 18)\) is on the line.