Equation of a straight line can be represented as y = mx + c where m is slope and c is y-intercept
slope, m of the line is calculated as follows:
[tex]\begin{gathered} slope,m\text{ = }\frac{\text{change in y}}{\text{change in x}} \\ \\ m\text{ = }\frac{-4-2}{-7-5} \\ m=\frac{-6}{-12} \\ m=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} to\text{ calculate the equation of the line:} \\ m\text{ = }\frac{1}{2},\text{ a point on the line is (5, 2)} \\ x1=\text{ 5, y1 =2 } \\ \text{ using y-y1=m(x-x1)} \\ y-2=\frac{1}{2}(x-5) \\ y-2=\frac{x}{2}-\frac{5}{2} \\ y\text{ = }\frac{x}{2}-\frac{5}{2}\text{ +2} \\ y\text{ = }\frac{x}{2}-\frac{1}{2} \\ \text{The equation of the line is }y\text{ = }\frac{x}{2}-\frac{1}{2} \end{gathered}[/tex]
The slope is 1/2
For the y-intercept:
Compare the equation with y = mx + c
c = -1/2
The y-intercept is -1/2
