Answer:
[tex]y=\frac{1}{2} x + \frac{7}{2}[/tex]
Step-by-step explanation:
Hi there!
We are given the points (5, 6) and (9, 8) that are contained in a line
We want to write the equation of this line 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, we need to find the slope of the line
The slope (m) can be found with the equation [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 on the line
We have everything we need to find the slope, but let's label the values of the points to avoid any confusion and mistakes when calculating
[tex]x_1=5\\y_1=6\\x_2=9\\y_2=8[/tex]
Now substitute into the formula
m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{8-6}{9-5}[/tex]
Subtract
m=[tex]\frac{2}{4}[/tex]
Simplify
m = 1/2
The slope of the line is 1/2
Substitute this into the formula (replace m with 1/2)
y = 1/2x + b
Now we need to find b
As the equation passes through both (5, 6) and (9, 8), we can use either one of those points to help solve for b
Taking (5,6) for example:
6 = 1/2(5) + b
Multiply
6 = 5/2 + b
Subtract 5/2 from both sides
7/2 = b
Substitute 7/2 as b into the equation
y = 1/2x + 7/2
Hope this helps!
Topic: finding the equation of the line
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