Answer:
[tex]y=2x-1[/tex]
Step-by-step explanation:
Use the slope-intercept formula: [tex]y=mx+b[/tex] where m is slope and b the y-intercept.
[tex](-2,-5)(4,7)[/tex]
Use the slope formula for when you have two points:
[tex]\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis. Insert values:
[tex]\frac{7-(-5)}{4-(-2)}[/tex]
Simplify parentheses (negative+negative=positive)
[tex]\frac{7+5}{4+2}[/tex]
Simplify
[tex]\frac{12}{6}=2[/tex]
2 is the slope:
[tex]y=2x+b[/tex]
Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:
(4,7)
[tex]y=2x+b\\7=2(4)+b[/tex]
[tex]7=8+b\\7-8=8-8+b\\7-8=b\\-1=b\\b=-1[/tex]
The y-intercept is -1. Insert into the equation. Change the + symbol to -:
[tex]y=2x-1[/tex]
Done.
