Question

Write an equation of the line that passes through the point and has the given slope. Use slope-intercept form. $$ (2,3), m=2 $$

Short answer

Hence, the equation of the line in slope-intercept form that passes through point (2,3) with a slope of 2 is \(y = 2x - 1\)

Step-by-step solution

Understand the Slope-Intercept Format

The slope-intercept form of a line's equation is \(y = mx + b\), where m is the slope and b is the y-intercept. In this case, m (the slope of the line) is given as 2.

Substitute the Point Values into Equation

Plug the given point (2,3), i.e., x = 2 and y = 3, into the equation. This should give us \(3 = 2*2 + b \).

Solve for the y-intercept

After substituting the point values, we have to solve the equation to find the value of b (the y-intercept). This will give us \(3 = 4 + b\). Solving this equation gives \(b = -1\).