Answer:
[tex]\textsf{C.} \quad y=mx[/tex]
Step-by-step explanation:
From inspection of the diagram, the graph is a linear.
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
- m is the slope
- b is the y-intercept
To find the slope of the line, define two points on the line:
- (x₁, y₁) = (x, y)
- (x₂, y₂) = (x + 1, y + m)
Substitute the defined points in the slope formula to find the slope (m):
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{(y+m)-y}{(x+1)-x}=\dfrac{m}{1}=m[/tex]
The y-intercept is the point at which the line intercepts the y-axis.
As the line passes through the origin (0, 0), the y-intercept is zero.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the given graph:
[tex]\implies y=mx[/tex]
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