Question

Write an equation in slope-intercept form of the line that passes through the point and has the given slope. $$ (-8,7), m=2 $$

Short answer

The equation in slope-intercept form of the line that passes through the given point (-8,7) and has the slope \(m = 2\) is \(y = 2x + 23\).

Step-by-step solution

Apply point and slope to the point-slope form

The point-slope equation of the line is given as: \(y - y_1 = m(x - x_1)\). Plug the point (-8,7) where \(x_1 = -8\) and \(y_1 = 7\), and the slope \(m = 2\) into the equation. Hence, the equation becomes: \(y - 7 = 2(x - -8) \).

Simplify the equation

Simplify \(x - -8\) to \(x + 8\) and distribute the slope value \(m = 2\) to the terms inside the parentheses. Therefore, the equation becomes: \(y - 7 = 2(x + 8)\) which simplifies to: \(y - 7 = 2x + 16\)

Transform into slope-intercept form

To change the equation into slope-intercept form \(y = mx + b\), add 7 to both sides of the equation. The equation becomes: \(y = 2x + 16 + 7\)

Final Simplification

Add the constant terms on the right side of the equation, that is 16 + 7 = 23. Thus, the final equation becomes: \(y = 2x + 23\) which represents in the form \(y = mx + b\).