Answer:
y=x-5
Step-by-step explanation:
Hi there!
We want to write an equation of the line that passes through the points (8,3) and (0,-5) in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope, and b is the y intercept
So let's first find the slope of the line
The formula for the slope calculated from two 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 needed to find the slope, but let's label the values of the points to avoid any confusion
[tex]x_1=8\\y_1=3\\x_2=0\\y_2=-5[/tex]
Now substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-5-3}{0-8}[/tex]
Subtract
m=[tex]\frac{-8}{-8}[/tex]
Simplify
m=1
The slope is 1
Here is the equation of the line so far:
y=1x+b (can also be written as y=x+b)
We need to find b
The equation passes through both (8, 3) and (0, -5), so we can substitute the values of either one of them as x and y to solve for b
Let's take (8, 3) for example
Substitute 8 as x and 3 as y
3=1(8)+b
Multiply
3=8+b
Subtract 8 from both sides
-5=b
Substitute -5 as b into the equation
y=x-5
Hope this helps!
