Question

If the equation of a line is \(y=\frac{1}{2} x+3\), then mark on the graph the point where the line crosses the \(y\)-axis and the point where the line crosses the \(x\)-axis.

Short answer

The line crosses the y-axis at the point (0, 3) and crosses the x-axis at the point (-6, 0).

Step-by-step solution

Find the y-intercept

To find the y-intercept, set x=0 in the equation and solve for y: \(y = \frac{1}{2}(0) + 3\) \(y = 3\) So, the y-intercept is at the point (0, 3).

Find the x-intercept

To find the x-intercept, set y=0 in the equation and solve for x: \(0 = \frac{1}{2}x + 3\) \(-3 = \frac{1}{2}x\) Now, multiply both sides by 2 to isolate x: \(-6 = x\) So, the x-intercept is at the point (-6, 0).

Plot the points on the graph

Plot the points (0, 3) and (-6, 0) on a Cartesian plane (graph). The point (0, 3) is where the line crosses the y-axis, and the point (-6, 0) is where the line crosses the x-axis.