Question

Write an equation of the line in slope-intercept form that passes through the two points, or passes through the point and has the given slope. $$(5,1), m=5$$

Short answer

The equation of the line in slope-intercept form is \(y = 5x - 24\).

Step-by-step solution

Understanding the formula

The slope-intercept form of a line is given by the equation \(y = mx + b\). In this equation, \(m\) represents the slope of the line, and \(b\) represents the y-intercept, which is the point at which the line intersects the y-axis.

Substituting the Given Values

Given that the slope of the line \(m = 5\) and one point on the line is \((5,1)\), we can substitute these values into the standard slope equation. By doing this, we now have the equation \(1 = 5 * 5 + b.\)

Solving for the y-intercept

Solving for \(b\) in the equation from Step 2 gives us \( b = 1 - 5 * 5\). Thus, \(b = -24\).

Writing the Final Equation

Substituting the values of \(m\) and \(b\) into the equation \(y = mx + b\), we get the final equation of the line: \(y = 5x - 24\).\n