Question

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(2,-4), m=-5$$

Short answer

The equation of the line in slope-intercept form is \(y = -5x + 6\).

Step-by-step solution

Insert the provided values into the slope-intercept formula.

Firstly, substitute the given values of the point and the slope into the slope-intercept equation \(y = mx + b\). This results in: \(-4 = -5*(2) + b\).

Simplify the equation in order to determine the y-intercept.

Next, simplify this equation. Multiply -5 (the slope) by 2 (the x-coordinate) to get -10. This results in: \(-4 = -10 + b\). Then, add 10 to both sides of the equation to solve for b: \(b=-4+10\).

Solve for the y-intercept.

Solve the equation for b. This results in: \(b = 6\).

Construct the final equation.

Now that the slope (m) and the y-intercept (b) are known values, they can be inserted into the slope-intercept equation. Therefore, the final equation of the line in slope-intercept form is: \(y = -5x + 6\).