Question

Use a table of values to graph the equation. \(y=-\frac{3}{4} x+1\)

Short answer

The graph of the equation \(y = -\frac{3}{4}x + 1\) is a straight line that slopes downward from left to right, intersecting the y-axis at y=1. This was confirmed after plotting the points (-2, 2.5), (0, 1), and (2, -0.5) obtained from our table of values.

Step-by-step solution

Identify the slope and y-intercept

The equation provided is \(y = -\frac{3}{4}x + 1\). Here, the number in front of x (-3/4) is the slope (m), and the constant at the end of the equation (1) is the y-intercept (b). Thus, for every 4 units that x increases, y will decrease by 3 units, and when x=0, y=1.

Construct a table of values

Choose a range of x values. For example, [-2, 0, 2]. Now substitute each x value into the equation to find the corresponding y value. For x=-2, substituting into the equation gives \(y = -\frac{3}{4}*(-2) + 1 = 2.5\). For x=0, \(y = -\frac{3}{4}*0 + 1 = 1\). For x=2, substituting gives \(y = -\frac{3}{4}*2 + 1 = -0.5\). Our table of values is thus as follows: (-2, 2.5), (0, 1), (2, -0.5).

Plot the points on a graph

The coordinate pairs from the table of values become points on the graph. Plot these points and draw a straight line through them. The line represents the equation. When you've plotted points (-2, 2.5), (0, 1), and (2, -0.5), a downward sloping straight line will emerge, which is accurate given the negative slope (-3/4) of the equation.