Question

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(5,-8), m=10$$

Short answer

The equation of the line in standard form is \(10x - y - 58 = 0\).

Step-by-step solution

Write the equation in slope-intercept form

The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We know the slope (\(m = 10\)) and a point on the line ((5, -8)). Plugging these values into the equation, we have \(-8 = 10 * 5 + b\), solving this for \(b\) will give the y-intercept.

Solve for b

Solving the equation \(-8 = 50 + b\) for \(b\) gives \(b = -8 - 50 = -58\). Thus, the equation in slope-intercept form is \(y = 10x - 58\).

Rewrite in standard form

The standard form of a linear equation is \(Ax + By = C\), where \(A, B,\) and \(C\) are integers, \(A\) and \(B\) are not both zero, and \(A\) is nonnegative. To rewrite the equation from slope-intercept form to standard form, we can move the terms around to get \(10x - y - 58 = 0\).