Answer
Option D is correct.
y = -¼(x)
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
b = 0 (the graph crosses the y-axis at 0)
To calculate the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]
For this question,
(x₁, y₁) and (x₂, y₂) are (-4, 1) and (4, -1)
[tex]\text{Slope = }\frac{-1-1}{4-(-4)}=\frac{-2}{4+4_{}}=\frac{-2}{8}=-\frac{1}{4}[/tex]
So, recall that
y = mx + b
m = slope = -¼
b = y-intercept = 0
y = mx + b
y = -¼x + 0
y = -¼(x)
Hope this Helps!!!
