Question

trazar la recta.
y=\frac{1}{4}x+5

Explanation:

Step1: Identify the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{1}{4}x + 5\), the y - intercept \(b = 5\). This means the line crosses the y - axis at the point \((0,5)\).

Step2: Use the slope to find another point

The slope \(m=\frac{1}{4}\), which can be interpreted as \(\frac{\text{rise}}{\text{run}}=\frac{1}{4}\). Starting from the point \((0,5)\), we can move up 1 unit (rise) and then move 4 units to the right (run) to get the next point. So, from \((0,5)\), adding 1 to the y - coordinate and 4 to the x - coordinate, we get the point \((0 + 4,5+1)=(4,6)\). We could also move down 1 unit and left 4 units from \((0,5)\) to get \((0 - 4,5 - 1)=(-4,4)\).

Step3: Plot the points and draw the line

Plot the points \((0,5)\) and \((4,6)\) (or \((-4,4)\) and \((0,5)\)) on the coordinate plane. Then, use a straight - edge to draw a line passing through these two points.

To draw the line:

1. Locate the point \((0,5)\) on the y - axis (since \(x = 0\) and \(y = 5\)).
2. From \((0,5)\), move 4 units to the right (along the x - axis) and 1 unit up (along the y - axis) to reach the point \((4,6)\).
3. Draw a straight line connecting \((0,5)\) and \((4,6)\) (and extend it in both directions).

Answer:

To draw the line \(y=\frac{1}{4}x + 5\), plot the y - intercept \((0,5)\) and use the slope \(\frac{1}{4}\) to find another point (e.g., \((4,6)\) or \((-4,4)\)) and draw a straight line through these points.