Answer & Step-by-step explanation:
Slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. Insert the given slope:
[tex]y=-5x+b[/tex]
To find the y-intercept, take the given coordinate point and insert:
[tex](-9_{x},-5_{y})\\\\-5=-5(-9)+b[/tex]
Solve for b:
Simplify multiplication:
[tex]-5=45+b[/tex]
Subtract 45 from both sides:
[tex]-50=b\\\\b=-50[/tex]
The y-intercept is -50. Insert:
[tex]y=-5x-50[/tex]
[tex]m=-5\\b=-50[/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]
The slope is the change in the y-axis over the change in the x-axis, or rise over run. Insert the points:
[tex](2_{x1},4_{y1})\\(10_{x2},2_{y2})[/tex]
[tex]\frac{2-4}{10-2}=\frac{-2}{8}=-\frac{2}{8}=-\frac{1}{4}[/tex]
The slope is [tex]-\frac{1}{4}[/tex] . Insert:
[tex]y=-\frac{1}{4}x+b[/tex]
Now follow the steps from the last problem to find the y-intercept. Choose a point and insert into the equation:
[tex](2_{x},4_{y})\\\\4=-\frac{1}{4}(2)+b[/tex]
Solve for b:
Simplify multiplication:
[tex]-\frac{1}{4}*\frac{2}{1}=-\frac{2}{4}=-\frac{1}{2}[/tex]
Re-insert:
[tex]4=-\frac{1}{2} +b[/tex]
Subtract b from both sides:
[tex]4-b=-\frac{1}{2} +b-b\\\\4-b=-\frac{1}{2}[/tex]
Subtract 4 from both sides:
[tex]4-4-b=-\frac{1}{2}-4\\\\-b=-\frac{1}{2}-4[/tex]
Simplify subtraction:
[tex]-\frac{1}{2}-4=-\frac{1}{2} -\frac{4}{1} =-\frac{1}{2} -\frac{8}{2} \\\\-\frac{1}{2} -\frac{8}{2}=-\frac{9}{2}[/tex]
Re-insert:
[tex]-b=-\frac{9}{2}[/tex]
Divide both sides by -1 to make the variable positive (can be seen as -1b):
[tex]b=\frac{9}{2}[/tex]
The y-intercept is [tex]\frac{9}{2}[/tex] .
Write the equation:
[tex]y=-\frac{1}{4}x+\frac{9}{2}[/tex]
:Done
