Complete the point-slope equation of the line through (3,6) and (5,-8). Use exact numbers. y-6=

Question

Complete the point-slope equation of the line through  (3,6) and  (5,-8). Use exact numbers.  y-6=

Bytelearn · Accepted Answer

Calculate Slope: First, we need to find the slope of the line that passes through the points (3,6) and (5,-8). The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Using the given points, we have m = (-8 - 6) / (5 - 3) = -14 / 2 = -7.Use Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We can use either of the given points for (x1, y1). Let's use the point (3,6). Substituting the slope and the coordinates of the point into the equation, we get y - 6 = -7(x - 3).Check Work: Finally, we can check our work by making sure the equation is in point-slope form and that it represents the line passing through the given points. The point-slope form is y - y1 = m(x - x1), and our equation is y - 6 = -7(x - 3), which matches the form. To check if the line passes through the points, we can substitute the x-coordinates of the given points into the equation and see if we get the corresponding y-coordinates. For (3,6), substituting x = 3 gives us y - 6 = -7(3 - 3) = -7(0) = 0, so y = 6, which is correct. For (5,-8), substituting x = 5 gives us y - 6 = -7(5 - 3) = -7(2) = -14, so y = -8, which is also correct.

Complete the point-slope equation of the line through $(3,6)$ and $(5,-8)$ . Use exact numbers. $\newline$ $y-6=$

Full solution

More problems from Write a linear equation from two points

Related topics

Complete the point-slope equation of the line through (3,6)(3,6)(3,6) and (5,−8)(5,-8)(5,−8). Use exact numbers.\newliney−6=y-6=y−6=

Complete the point-slope equation of the line through $(3,6)$ and $(5,-8)$ . Use exact numbers. $\newline$ $y-6=$