Question

Write an equation of the line in slope-intercept form that passes through the two points, or passes through the point and has the given slope. $$(4,-5),(-1,-3)$$

Short answer

The equation of the line in slope-intercept form that passes through the points (4,-5) and (-1,-3) is \(y = -0.4x - 3.4\).

Step-by-step solution

Calculate the slope

The slope (m) of a line passing through the coordinates \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula \(m = (y_2 - y_1) / (x_2 - x_1)\). For the points given in the exercise, which are \((4, -5)\) and \((-1, -3)\), the slope can be calculated as \(m = (-3 - (-5)) / (-1 - 4) = 2 / -5 = -0.4\).

Calculate the y-intercept

Now the y-intercept (b) can be calculated. From the slope-intercept equation \(y = mx + b\), we get \(b = y - mx\). Substituting one of the points and the calculated slope, \(b = -5 - (-0.4 * 4) = -5 + 1.6 = -3.4\).

Write the final equation

By substituting the slope and y-intercept values into the slope-intercept form we get the equation of the line, \(y = -0.4x - 3.4\).