Question

a line is graphed in the xy - plane shown. which of the following is an equation of the line? choose 1 answer: a $y=\frac{3}{7}x + 1$ b $y=\frac{3}{7}x - 1$ c $y=-\frac{3}{7}x + 1$ d $y=-\frac{3}{7}x - 1$

Explanation:

Step1: Determine the slope

The line is increasing, so the slope \(m\) is positive. The slope - formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). If we assume two points on the line \((x_1,y_1)\) and \((x_2,y_2)\), say the \(y\) - intercept \((0,b)\) and another point. The line rises about 3 units for every 7 units it runs to the right, so \(m = \frac{3}{7}\).

Step2: Determine the y - intercept

The line crosses the \(y\) - axis at the point \((0,1)\), so the \(y\) - intercept \(b = 1\).

Step3: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. Substituting \(m=\frac{3}{7}\) and \(b = 1\) into the equation, we get \(y=\frac{3}{7}x+1\).

Answer:

A. \(y=\frac{3}{7}x + 1\)