Answer:
y = -1/2x + 19/2
Step-by-step explanation:
Hi there!
We are given the points (9,5) and (7,6)
We want to write an equation of the line that contains these two points, in slope-intercept form
Slope-intercept form is given 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 any confusion.
[tex]x_1=9\\y_1=5\\x_2=7\\y_2=6[/tex]
Now 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}{7-9}[/tex]
Subtract
m=[tex]\frac{1}{-2}[/tex]
m=-1/2
The slope of the line is -1/2
We can substitute this as m into the formula for slope-intercept form:
y = -1/2x + b
Now we need to find b
As the equation passes through (9, 5) and (7, 6), we can use either one to solve for b
Taking (7, 6) for example:
Substitute 7 as x and 6 as y into the equation
6 = -1/2(7) + b
Multiply
6 = -7/2 + b
Add 7/2 to both sides
19/2 = b
substitute 19/2 as b:
y = -1/2x + 19/2
Hope this helps!
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