Question

incorrect your answer is incorrect. find an equation for the line that passes through the points (5, 3) and (-4, 6). try again

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For the points \((5, 3)\) and \((-4, 6)\), we have \( x_1 = 5 \), \( y_1 = 3 \), \( x_2 = -4 \), \( y_2 = 6 \). So, \( m = \frac{6 - 3}{-4 - 5} = \frac{3}{-9} = -\frac{1}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \). Let's use the point \((5, 3)\). Substituting \( m = -\frac{1}{3} \), \( x_1 = 5 \), and \( y_1 = 3 \) into the point - slope form, we get \( y - 3 = -\frac{1}{3}(x - 5) \).

Step3: Convert to slope - intercept form (optional, but to get a more standard form)

Expand the right - hand side: \( y - 3 = -\frac{1}{3}x+\frac{5}{3} \). Then, add 3 to both sides. Since \( 3=\frac{9}{3} \), we have \( y = -\frac{1}{3}x+\frac{5}{3}+\frac{9}{3}=-\frac{1}{3}x+\frac{14}{3} \). We can also write it in standard form \( x + 3y=14 \) (by multiplying both sides by 3: \( 3y=-x + 14\), then \( x+3y = 14\)).

Answer:

One equation of the line is \( y=-\frac{1}{3}x+\frac{14}{3} \) (or \( x + 3y = 14 \))