Answer:
[tex]y=-x+9[/tex]
Step-by-step explanation:
This is asking you to write the equation in slope-intercept form:
[tex]y=mx+b[/tex]
where:
- m is the slope
- b is the y-intercept
- x and y are any corresponding coordinate points (x,y)
You need to find the slope of the two given points using:
[tex](x_{1},y_{1})\\\\(x_{2},y_{2})\\\\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=slope[/tex]
Insert the values:
[tex](4_{x_{1}},5_{y_{1}})\\\\(-6_{x_{2}},15_{y_{2}})\\\\\frac{15-5}{-6-4} =\frac{10}{-10} =-\frac{10}{10} =-1[/tex]
The slope of the given line is -1. Insert this value into the equation:
[tex]y=-1x+b\\\\y=-x+b[/tex]
Now insert one of the given coordinate points as x and y to solve for b:
[tex](4_{x},5_{y})\\\\5=-4+b\\\\5+4=-4+4+b\\\\9=b[/tex]
The y-intercept is 9. Insert the value:
[tex]y=-x+9[/tex]
:Done
