Question

Graph the line that passes through the points. Write its equation in slope- intercept form. (Review \(5.3 \text { for } 5.7)\) $$(2,9),(4,7)$$

Short answer

The equation of the line that passes through the points (2,9) and (4,7) in slope-intercept form is \(y = -1x + 11\).

Step-by-step solution

- Calculate the Slope

First, calculate the slope (m) of the line using the formula: \(m = (y2 - y1) / (x2 - x1)\). For the points (2,9) and (4,7), this would be: \(m = (7 - 9) / (4 - 2) = -2 / 2 = -1\).

- Calculate the y-intercept

Substitute one of the given points and the slope into the slope-intercept equation to solve for b. Using the point (2,9) and m = -1, the equation becomes: \(9 = -1 * 2 + b\). Solving for b gives: \(b = 9 + 2 = 11\).

- Write the Equation of the Line

Now that we have calculated the slope and y-intercept, we can write the equation of the line in slope-intercept form. Substituting m = -1 and b = 11 into the equation \(y = mx + b\) gives the equation of the line as: \(y = -1x + 11\).