Question

Graph the line that passes through the points. Write its equation in slope- intercept form. (Review \(5.3 \text { for } 5.7)\) $$(2,3),(-4,1)$$

Short answer

The equation of the line passing through the points (2,3) and (-4,1) is \(y = 1/3x + 7/3\)

Step-by-step solution

Calculate the slope

Use the formula \(m = (y_2 - y_1) / (x_2 - x_1)\) to find the slope of the line. For the given points (2,3) and (-4,1), the slope \(m\) can be calculated as \(m = (1-3) / (-4-2) = -2 / -6 = 1/3\).

Find the y-Intercept

The y-intercept can be found using the equation of the line in slope-intercept form: \(y = mx + b\). Substituting the coordinates of any point on the line and the calculated slope into this equation, one can find the value of \(b\). For example, using the point (2,3) and slope \(1/3\), the equation becomes \(3 = 1/3 * 2 + b\). Solving for \(b\), we find \(b = 3 - 2/3 = 7/3\).

Write the Equation of the Line

The equation of the line in slope-intercept form is \(y = mx + b\). So, substituting the calculated slope, \(m = 1/3\), and y-intercept, \(b = 7/3\), into the equation gives the final equation \(y = 1/3x + 7/3\).