Use 2 points from the chart to find the equation of the line. 

Example: (–1, 3) and (1, –1)  

Using the formula for the slope, we find the slope to be –2.  Putting that into our equation for a line we get y = –2x + b.  Plug in one of the points for x and y into this equation in order to find b.  b = 1.  

The equation then will be: y = –2x + 1. 

Plug in 5 for x in order to find y.  

y = –2(5) + 1  

y = –9

The slope of a line is defined as a change in the y coordinates over a change in the x coordinates (rise over run).

To calculate the slope of a line, use the following formula: 

The slope of the line that passes these two points are simply ∆y/∆x = (3-5)/(2+3) = -2/5

The slope is negative as it starts in quadrant 2 and ends in quadrant 4. Slope is equivlent to the change in y divided by the change in x. The change in y is greater than the change in x, which implies that the slope must be less than –1, leaving –2 as the only possible solution.

Let \(\displaystyle P_{1}=(8,3)\) and \(\displaystyle P_{2}=(5,7)\)

\(\displaystyle m = (y_{2} - y_{1}) \div (x_{2} - x_{1})\) so the slope becomes \(\displaystyle -\frac{4}{3}\).

\(\displaystyle \textup{Get into }y=mx+b\textup{ format: }3y=-2x+6\:,\:y=-\frac{2}{3}x+2\)

\(\displaystyle \textup{Perpendicular slope is negative reciprocal of }-\frac{2}{3}\: \rightarrow \rightarrow \frac{3}{2}\)

The slope of a line. given two points \(\displaystyle (x_{1}, y_{1}), (x_{2}, y_{2})\) can be calculated using the slope formula

\(\displaystyle m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}\)

Set \(\displaystyle x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18\):

\(\displaystyle m = \frac{18-0}{0-(-6)} = \frac{18}{3} = 3\)

For each equation, solve for \(\displaystyle y\) and express in the slope-intercept form \(\displaystyle y=mx + b\). The coefficient of \(\displaystyle x\) will be the slope.

\(\displaystyle 4x+y = 7\)

\(\displaystyle 4x+y- 4x = 7 - 4x\)

\(\displaystyle y = -4x + 7\)

Slope: \(\displaystyle m = -4\)

\(\displaystyle 4y + x = 7\)

\(\displaystyle 4y + x- x = 7 - x\)

\(\displaystyle 4y = -x + 7\)

\(\displaystyle \frac{4y}{4} =\frac{ -x + 7}{4}\)

\(\displaystyle y = - \frac{1}{4}x + \frac{7}{4}\)

Slope: \(\displaystyle m = - \frac{1}{4}\)

\(\displaystyle 4y = x + 7\)

\(\displaystyle \frac{4y}{4} =\frac{ x + 7}{4}\)

\(\displaystyle y = \frac{1}{4}x + \frac{7}{4}\)

Slope: \(\displaystyle m = \frac{1}{4}\)

\(\displaystyle 4x= y + 7\)

\(\displaystyle 4x- 7= y + 7 - 7\)

\(\displaystyle y = 4x - 7\)

Slope: \(\displaystyle m = 4\). 

The line of the equation 

\(\displaystyle 4x= y + 7\)

is the one with slope 4.

While solving the problem requires the same method as the ones above, this is one is more complicated because of the more complex given equations. Start of by deriving a substitute for one of the unknowns. From the second equation we can derive y=75-(5x/2). Since 2y = 150 -5x, we divide both sides by two and find our substitution for y. Then we enter this into the first equation. We now have –x-4(75-(5x/2))=245. Distribute the 4. So we get –x – 300 + 10x = 245. So 9x =545, and x=545/9. Use this value for x and solve for y. The graph below illustrates the solution.