Question

graphing an equation in slope-intercept form
graph: $y = \frac{3}{4}x + 5$
click or tap the graph to plot a point.

Explanation:

Step1: Identify slope-intercept form

The equation \( y = \frac{3}{4}x + 5 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{3}{4} \) (slope) and \( b = 5 \) (y - intercept). So the y - intercept is at \( (0,5) \). We can plot this point first.

Step2: Find another point using slope

The slope \( m=\frac{3}{4}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,5) \), we move up 3 units (rise) and then 4 units to the right (run). So the new point is \( (0 + 4,5+3)=(4,8) \). We can also find a point by substituting \( x=- 4 \) into the equation: \( y=\frac{3}{4}\times(-4)+5=-3 + 5 = 2 \), so the point is \( (-4,2) \).

Step3: Plot the points and draw the line

Plot the points \( (0,5) \), \( (4,8) \), and \( (-4,2) \) on the graph and then draw a straight line passing through these points. Also, for the table:

• When \( x = 0 \), \( y=\frac{3}{4}(0)+5 = 5 \)
• When \( x = 4 \), \( y=\frac{3}{4}(4)+5=3 + 5 = 8 \)
• When \( x=-4 \), \( y=\frac{3}{4}(-4)+5=-3 + 5 = 2 \)

\( x \)	\( y \)
\( 4 \)	\( 8 \)
\( - 4 \)	\( 2 \)

Answer:

To graph \( y=\frac{3}{4}x + 5 \):

1. Plot the y - intercept \( (0,5) \) (since \( b = 5 \) in \( y=mx + b \)).
2. Use the slope \( \frac{3}{4} \) to find other points (e.g., from \( (0,5) \), move 3 up and 4 right to get \( (4,8) \), or 3 down and 4 left to get \( (-4,2) \)).
3. Draw a straight line through the plotted points. The table of values can be filled as shown above.