Answer:
[tex]y=4x+20[/tex]
Step-by-step explanation:
To write an equation, use the slope-intercept equation:
[tex]y=mx+b[/tex]
M is the slope and b is the y-intercept.
First, find the slope by using 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. Substitute values:
[tex](-5,0)(-4,4)\\(-5(x1),0(y1))\\(-4(x2),4(y2))\\\\\frac{4-0}{-4-(-5)}[/tex]
Simplify parentheses (two negatives make a positive) and simplify:
[tex]\frac{4-0}{-4+5}\\\\\frac{4}{1}=4[/tex]
The slope, m, is 4. Insert this information into the equation:
[tex]y=4x+b[/tex]
Now, take one of the points and insert into the slope-intercept formula:
[tex](-5,0)\\(-5(x),0(y))\\\\0=4(-5)+b[/tex]
Solve for b, the y-intercept. Simplify multiplication:
[tex]0=-20+b[/tex]
Add 20 to both sides and simplify:
[tex]0+20=-20+20+b\\20=b\\b=20[/tex]
The y-intercept, b, is 20. Insert this value into the equation:
[tex]y=4x+20[/tex]
Done.
