1. Sketch the graph of the equation 2y + 3x = 1. Help with Steps Please? Anyone?
2. Determine the equation of the straight line through the point (-1, 5) with slope m = -1. Steps?
"1. Sketch the graph of the equation 2y + 3x = 1"
As this equation represents a line, finding two points and drawing the line through them will be enough. I would find the points where the line crosses the axes.
$\displaystyle 2y + 3x = 1$
If I take $\displaystyle y=0$,
the equation will be, $\displaystyle 0 + 3x = 1$,
$\displaystyle x=\frac{1}{3}$
So the point is $\displaystyle \left(\frac{1}{3},0\right)$
Similarly, If I take $\displaystyle x=0$,
the equation becomes, $\displaystyle 2y + 0 = 1$,
$\displaystyle y=\frac{1}{2}$
So the point is $\displaystyle \left(0,\frac{1}{2}\right)$
Now you can draw the axes, put the points and draw the line that passes on them.
"2. Determine the equation of the straight line through the point (-1, 5) with slope m = -1."
The general equation of line is $\displaystyle y = m\cdot x + C$. m is the slope of the line and C is a constant. Now, using the information given in the question, try to find C. Then there you found the equation