Answer:
[tex]y = \frac{5}{4} x -1[/tex]
Step-by-step explanation:
Find the slope of this line by using the slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute both given points into this formula.
[tex]\frac{(-6)-(4)}{(-4)-(4)} \rightarrow\frac{-10}{-8} \rightarrow\frac{-5}{-4} =\frac{5}{4}[/tex]
The slope of the line is 5/4. Now this can be plugged into point-slope form since we have the point and the slope of the line.
Use any pair of given points, I'll be using (4,4).
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex]
Substitute 4 for [tex]x_1[/tex], 4 for [tex]y_1[/tex], and 5/4 for m.
[tex]y-(4)=\frac{5}{4} (x-(4))[/tex]
Simplify this equation.
[tex]y-4=\frac{5}{4} (x-4)\rightarrow y-4=\frac{5}{4} x-5\rightarrow y = \frac{5}{4} x -1[/tex]
The equation in slope-intercept form of the line is [tex]y = \frac{5}{4} x -1[/tex].
