Answer:
y = -x + 7
Step-by-step explanation:
Hi there!
We are given the following points:
(5,2) and (10,-3)
We want to find the equation of the line that passes through these 2 points
There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b (m is the slope and b is the y intercept).
First, let's find the slope of the line.
The slope can be calculated from 2 points using 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
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=5\\y_1=2\\x_2=10\\y_2=-3[/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{-3-2}{10-5}[/tex]
Simplify
m=[tex]\frac{-5}{5}[/tex]
Divide
m=-1
The slope of the line is -1
We can substitute this value as m in y=mx+b.
Here's the equation of our line so far:
y=-x+b
Now we need to find b
As the equation passes through the points (5,2) and (10,-3), we can use either point to find the value of b
Taking (5,2) for example:
Substitute 5 as x and 2 as y
2=-5+b
Add 5 to both sides
7=b
Substitute 7 as b in the equation
y = -x + 7
Hope this helps!
See more on this topic here: https://brainly.com/question/27166723
