Answer:
y = -x +4
Step-by-step explanation:
Hi there!
We are given the equation of a line, and we want to write the equation of this line in slope-intercept form
Slope-intercept form is written as y=mx+b, where m is the slope and b is the value of y at the y-intercept
First, we need to find the slope of the line
The slope (m) can be calculated from 2 points, 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
First, let's find 2 points on the line:
The intercepts - the points where the line hits the x and y axis are a good place to start; the intercepts of this line are (4,0) and (0, 4), which will also work for calculating the slope
Let's label the values of these 2 points to avoid any confusion and mistakes when calculating.
[tex]x_1=4\\y_1=0\\x_2=0\\y_2=4[/tex]
Substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{4-0}{0-4}[/tex]
Subtract
m=[tex]\frac{4}{-4}[/tex]
Divide
m = -1
The slope of the line is -1
We can substitute that into our equation:
y = -x + b (when -1 is the leading coefficient, only adding a minus sign in front of the variable will suffice)
Now we need to find b
As said earlier, b is the value of y at the y intercept
The point of the y intercept is (0, 4), and the value of y at this point is 4
So substitute 4 as b into the equation
y = -x + 4
Hope this helps!
