# Thread: Deceptively simple looking . . .

1. ## Deceptively simple looking . . .

Hello! I'm kind of new to this forum, and I hope I'm posting in the right category. My school calls the class I'm taking "College Algebra", but I've been told by some that it's roughly equal to Pre-Calc.

My question on this worksheet looks simple on the surface, but I never seem to get the right answer (-4/5) and it'd be nice to know why. Here it is:

Find the value of a if the line through (-1, a) and (3, -4) is parallel to y=ax.

What I've been doing is plugging (3, -4) into the equation as the x- and y-values, but that gets me the answer -4/3, which is not quite right.

Any suggestions?

2. Originally Posted by potato92
Hello! I'm kind of new to this forum, and I hope I'm posting in the right category. My school calls the class I'm taking "College Algebra", but I've been told by some that it's roughly equal to Pre-Calc.

My question on this worksheet looks simple on the surface, but I never seem to get the right answer (-4/5) and it'd be nice to know why. Here it is:

Find the value of a if the line through (-1, a) and (3, -4) is parallel to y=ax.

What I've been doing is plugging (3, -4) into the equation as the x- and y-values, but that gets me the answer -4/3, which is not quite right.

Any suggestions?
First note the point is not on the line. However the slope of the line is $m=a$

Also since you have two points you can use the relation

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

Now just set the two eqaul and solve for a.

3. Yes, "plugging" the points into the equation y= ax will not give you anything because those points are NOT on that line- they are on a line parallel to that line.

Another way to do this- any non-vertical line can be written in the form y= mx+ b where "m" is the slope and b is the y-intercept. The slope of line y= ax is a and any line parallel to it will have slope a also. So you know your line has equation y= ax+ b.

Put x= 3, y= -4 into that equation to determine and equation for a and b. Put x= -1, y= a to get a second equation for a and b.

solve those equations for a and b and write out the equation of the line.