Answer:
a) (-2,0) is the x-intercept of the line.
b) (0,4) is the y-intercept of the line.
c) "2" is the slope of the line.
d) 2x + 4 = y (Equation of the Line)
Explanation:
All linear equations have a general form: mx+n.
When we figure out two points on the line, we can use them in this general formula and find out the equation for the line.
We can use x and y intercepts of the line for that, they are also asked to find.
The x-intercept of the line is (-2,0) because this is where the line crosses the x axis, this point is named as x-intercept.
Except the axis, y-intercept has no more difference than x-intercept. So, the y-intercept of a line is where the line crosses the y axis.
We can see that the line crosses y axis at (0,4).
Now, we know two specific points on the line. This means that we can find the slope and write the equation for this line.
We can find the slope using the formula below:
y1 - y0 / x1 - x0 = Slope
This would give us the slope for the line, no matter which point you take as (x1, y1). The order is not important.
If you use the given points on the formula above, you would get "2" as the slope of the line.
In the general form of a linear equation, the coefficient of "x" is equal to the slope of the line. This means that "m" is equal to "2". (y = 2x + n)
Finally, you can use one of the known points to find out the real equation for the line.
Let's use (0,4):
2x + n = y (Use 0 for "x" and 4 for "y" variable.)
We can conclude that "n" is equal to 4.
So, the equation of this line is equal to "2x + 4 = y".