Question

Find an equation of the line that passes through the point and has the indicated slope. Sketch the line. $$ \frac{\text { Point }}{(0,3)} \quad \frac{\text { Slope }}{m=\frac{3}{4}} $$

Short answer

The equation of the line that passes through the point (0,3) and has a slope of 3/4 is \(y = 3/4x + 3\). The line can be sketched on an x-y graph by marking the y-intercept at (0,3) and utilizing the slope (rise over run) to find other points on the line.

Step-by-step solution

Insert the given point and slope into the point-slope form of the line equation

By inserting \(x_1 = 0\), \(y_1 = 3\), and \(m = 3/4\) into the point-slope equation \(y - y_1 = m(x - x_1)\), the equation becomes \(y - 3 = 3/4 * (x - 0)\).

Simplify the equation

This simplifies to \(y - 3 = 3/4x\). Adding 3 to both sides to isolate \(y\), we get the equation of the line as \(y = 3/4x + 3\).

Sketch the line

Draw an x-y graph. Mark a point at (0, 3) which is the y-intercept. Since the slope of the line is 3/4, from the y-intercept, move 3 units up (the rise) and 4 units to the right (the run). Draw the line that passes through these points.