Answer:
y = 4x + 3
Step-by-step explanation:
We are given the line shown in your question.
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 value of y at the y intercept
As we are given the graph of the line, we can pick any 2 points to help us find the equation; in this case, let's take (0,3) and (-1, -1).
First, we need to find the slope of the line
The slope (m) can be found 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
Let's label the values of the points to avoid confusion and mistakes before calculating.
[tex]x_1= 0\\y_1=3\\x_2=-1\\y_2=-1[/tex]
Now substitute these values into the equation for the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-1-3}{-1-0}[/tex]
Subtract
m=[tex]\frac{-4}{-1}[/tex]
Divide
m = 4
The slope of the line is 4
Here is the equation of the line so far:
y = 4x + b
Now we need to find b
As stated above, b is the value of y at the y intercept; the y intercept is the point where the line intersects with the y axis. The value of x at this point is 0
One of the points we used to calculate the slope was actually the y intercept point; this point is (0, 3). The value of y at this point is 3, so the value of b is 3
Substitute 3 as b in our equation
y = 4x + 3
Topic: finding the equation of the line
