Question

1. $y = \frac{3}{4}x + 3$

Explanation:

Step1: Identify the y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=\frac{3}{4}x + 3\), when \(x = 0\), \(y=3\). So the line passes through the point \((0,3)\), which is already marked on the graph.

Step2: Use the slope to find another point

The slope \(m=\frac{3}{4}\), which means for a run (change in \(x\)) of \(4\) units, the rise (change in \(y\)) is \(3\) units. Starting from the y - intercept \((0,3)\), if we move \(x = 4\) (run = 4) and \(y=3\) (rise = 3), we get the point \((0 + 4,3+3)=(4,6)\).

Step3: Plot the points and draw the line

Plot the points \((0,3)\) and \((4,6)\) (or we can use another set of points. For example, if we take \(x=- 4\), then \(y=\frac{3}{4}\times(-4)+3=-3 + 3=0\), so the point \((-4,0)\) is also on the line). Then draw a straight line passing through these points.

(If the task was to graph the line, the steps above show how to plot the line. If it was to find some property like slope or intercept, we can also state that the slope \(m = \frac{3}{4}\) and y - intercept \(b = 3\))

Answer:

To graph \(y=\frac{3}{4}x + 3\):

1. Plot the y - intercept \((0,3)\) (already marked).
2. Use the slope \(\frac{3}{4}\): from \((0,3)\), move 4 units right and 3 units up to get \((4,6)\) (or 4 units left and 3 units down to get \((-4,0)\)).
3. Draw a straight line through the plotted points.

(If the question was about slope or intercept: Slope \(=\frac{3}{4}\), Y - intercept \(=3\))