Question

Write an equation in slope-intercept form of the line that passes through the points. $$ (5,-10),(12,-7) $$

Short answer

The equation of the line in slope-intercept form that passes through the given points is \(y = 3/7x -12.1428\)

Step-by-step solution

Calculation of the Slope

First, using the formula for the slope \((m)\) of a line passing through two points \((x1,y1)\) and \((x2, y2)\), we calculate that as follows: \(m = (y2-y1)/(x2-x1) = (-7 - (-10))/(12-5) = 3/7\). Thus, the slope of the line is \(3/7\).

Calculation of the y-Intercept

Next, substitute the slope and one set of the coordinates into the slope-intercept form \((y=mx+c)\). Doing this gives us \(-10 = (3/7) * 5 + c\). Solving for \(c\) we get the value: \(c = -10 - 15/7 = -70/7 - 15/7 = -85/7 = -12.1428\).

Write the Equation of the Line

Now, substitute the calculated slope and y-intercept into the slope-intercept form to get the equation of the line. After substitution, the equation of the line will be \(y = 3/7x -12.1428\).