Answer :
Answer:
y=x-1
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the points (7, 6) and (-2, -3)
There are 3 ways to write the equation of the line:
- Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
- Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
- Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative
The most common (and usually, the easiest way) would be slope-intercept form, so let's write it that way
First, we'll need to find the slope of the line
The slope can be found using the formula [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 two points, which is needed, but let's label their values in order to avoid any confusion:
[tex]x_1= 7\\y_1=6\\x_2=-2\\y_2=-3[/tex]
Now substitute these values into the formula to find the slope (m):
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-3-6}{-2-7}[/tex]
Subtract the numbers
m=[tex]\frac{-9}{-9}[/tex]
Divide
m=1
The slope of the line is 1
So far, we can write the equation of the line as this:
y=1x+b, or y=x+b
We'll need to find b
As the equation passes through both (7,6) and (-2, -3), we can use either one of them to solve for b
Taking (7, 6) for instance, substitute 7 as x and 6 as y:
6=1(7)+b
Multiply
6=7+b
Subtract 7 from both sides
-1=b
Now substitute -1 as b:
y=x-1
Hope this helps!