Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=33x
y equals Start Fraction 3 over 3 End Fraction x
y=8x
y equals 8 x
y=3x
y equals 3 x
y=x
y equals x
To derive the equation in slope-intercept form, which is y = mx, we need to find the slope of the line.
Looking at the graph, we can see that the line passes through the origin (0, 0). This means the y-intercept (b value) is 0.
To find the slope (m value), we can choose any two points on the line and use the formula: m = (y2 - y1) / (x2 - x1).
Let's choose two points on the line:
Point 1: (0, 0)
Point 2: (1, 1)
Plugging these values into the slope formula:
m = (1 - 0) / (1 - 0)
m = 1 / 1
m = 1
Therefore, the equation for the line through the origin is simplified as:
y = 1x
Simplifying the numerical coefficient, 1x can be written as just x.
So, the final equation is:
y = x