Answer:
y=3x-1
Step-by-step explanation:
Hi there!
We are given a line, and we want to find the equation of that 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 of the line can be calculated from 2 points 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
We can take any 2 points from the line to help us; for example, we can take (0,-1), and (1,2), which are both on the line
We can label the values of the points to avoid confusion while we calculate the slope:
[tex]x_1=0\\y_1=-1\\x_2=1\\y_2=2[/tex]
Now let's plug these values into the formula to solve for the slope:
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{2--1}{1-0}[/tex]
Simplify:
m=[tex]\frac{2+1}{1-0}[/tex]
Add/subtract:
m=[tex]\frac{3}{1}[/tex]
m=3
The slope of the line is 3
Remember that our equation is y=mx+b; we can plug 3 as m into the equation right now.
This is our equation so far:
y=3x+b
Now we need to find b
The y intercept (b) is the point in where the line intersects with the y axis; the value of x is 0 at that point
Since we have the graph given, we can find the value of the y intercept by finding the point that crosses (intersects) the y axis.
That point would be (0, -1)
The value of b is simply the value of y at this point; in this case, the value of b is -1
So plug -1 as b into the equation:
y=3x-1
Hope this helps!
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