Answer:
[tex]y=\frac{1}{10}x + 7[/tex]
Step-by-step explanation:
Hi there!
We are given the points (-20, 5) and (-10, 6)
We want to write the equation of the line in slope-intercept form
Slope-intercept form can be written as y=mx+b, where m is the slope, and b is the y intercept
First, let's find the slope of the line
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes
[tex]x_1=-20\\y_1=5\\x_2=-10\\y_2=6[/tex]
Substitute these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{6-5}{-10--20}[/tex]
Simplify
m=[tex]\frac{1}{-10+20}[/tex]
m=[tex]\frac{1}{10}[/tex]
The slope (m) of the line is 1/10
We can substitute this value into the formula y=mx+b
y = [tex]\frac{1}{10}x[/tex] + b
Now we need to solve for b
As the equation passes through the points (-20, 5) and (-10, 6), we can use either point to solve for b.
Taking (-20, 5) for instance:
Substitute -20 as x and 5 as y:
5=[tex]\frac{1}{10}(-20)[/tex] + b
Multiply
5=-2+b
Add 2 to both sides
7=b
Substitute 7 as b.
y=[tex]\frac{1}{10}x + 7[/tex]
Hope this helps!
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