Question

40 multiple choice 1 point

1. write an equation for the line graphed.

a) y = 2
b) y = 2x
c) y = -2x
d) y = 2x + 1
graph of a line passing through the origin with positive slope
options: c, d, b, a

Explanation:

Step1: Analyze the line's features

The line passes through the origin \((0,0)\), so the \(y\)-intercept \(b = 0\). The slope \(m\) can be calculated. For a line through \((0,0)\) and another point, say \((1,2)\) (from the graph, when \(x = 1\), \(y = 2\)), slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 0}{1 - 0}=2\).

Step2: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). With \(m = 2\) and \(b = 0\), the equation is \(y = 2x\).

Step3: Eliminate other options

• Option A: \(y = 2\) is a horizontal line, not matching the graphed line.
• Option C: \(y=-2x\) has a negative slope, but the graphed line has a positive slope.
• Option D: \(y = 2x+1\) has a \(y\)-intercept of \(1\), but the line passes through \((0,0)\), so \(b

eq1\).

Answer:

B. \(y = 2x\)