Given:
A line passes throught the point (-1,6).
The slope of the line is m = (5/4).
The objectiv is to find the equation of the line.
Explanation:
Consider the coordinates as,
[tex](x_1,y_1)=(-1,6)_{}[/tex]The general formula to fid the equation of line in slope-point form is,
[tex]y-y_1=m(x-x_1)\text{ . }\ldots\ldots\ldots(1)[/tex]Now, substitue the given values in equation (1).
[tex]\begin{gathered} y-6=\frac{5}{4}(x-(-1)) \\ y-6=1.25(x+1) \\ y=1.25x+1.25+6 \\ y=1.25x+7.25\text{ . . . .(2)} \end{gathered}[/tex]To obtain the graph:
Consider two value for the x = 0 and y = 0 to obtain coordinates to draw the graph.
At x = 0:
Substitute the value of x in equation (2),
[tex]\begin{gathered} y=1.25(0)+7.25 \\ y=7.25 \end{gathered}[/tex]Thus, the coordinate is (0,7.25).
At y = 0:
Substitute the value of y in equation (2),
[tex]\begin{gathered} 0=1.25x+7.25 \\ x=\frac{-7.25}{1.25} \\ x=-5.8 \end{gathered}[/tex]Thus, the coordinate is (-5.8,0).
To plot the graph:
The graph of the line will be,
Hence, the graph of the line y = 1.25x + 7.25 is obtained.
