Question

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. $$(0,4), m=3$$

Short answer

The point-slope form of the equation is \(y - 4 = 3x\) and the slope-intercept form is \(y = 3x + 4\).

Step-by-step solution

Identify given point and slope

The given point is (0,4) and the slope \(m\) is 3.

Substitute into the point-slope formula

Apply the point-slope formula \(y-y_1=m(x-x_1)\). Here, \(x_1 = 0\), \(y_1 = 4\) and \(m = 3\). Thus, substituting these values yields the point slope-form equation \(y - 4 = 3(x - 0)\). When simplified, this gives \(y - 4 = 3x\).

Convert into slope-intercept form.

Rearrange the equation into the slope-intercept form \(y = mx + b\). This involves getting \(y\) by itself on one side of the equation: \(y = 3x + 4\).