Question

two lines, m and q, are shown in the graph below. line m has the same y-intercept as ______. options: line q, y = 2x - 3, y = -3x

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a line is the point where it crosses the y - axis (when \(x = 0\)). For a linear equation in the form \(y=mx + b\), \(b\) is the y - intercept.

Step2: Analyze line m's y - intercept

From the graph, line \(m\) crosses the y - axis at \((0,- 3)\), so its y - intercept is \(-3\).

Step3: Analyze each option

• For "line q": We need to check its y - intercept from the graph. But visually, line \(q\) has a different y - intercept (it seems to cross the y - axis at a different point, likely not \(-3\)).
• For \(y = 2x-3\): In the slope - intercept form \(y=mx + b\), here \(b=-3\), so its y - intercept is \(-3\).
• For \(y=-3x\): In the slope - intercept form \(y = mx + b\), here \(b = 0\), so its y - intercept is \(0\).

Answer:

\(y = 2x-3\)