Question

Graph the equation and find the x-coordinate of the x-intercept:1.5x - 3y = 7Round to the nearest hundredth

Answer 1

We can begin by finding the x-intercept. This is the point at which the graph crosses the horizontal axis. This point is given when the y-value of the function is 0, then, we can solve the equation for y = 0 and find the value for x:

`\begin{gathered} 1.5x-3y=7\to y=0 \\ 1.5x-3\cdot(0)=7 \\ 1.5x=7 \\ x=(7)/(1.5) \\ x\approx4.67 \end{gathered}`

The x value of the x-intercept of the equation is approximately 4.67.

This is a linear equation, to build the graph we just need 2 points and join them with the line.

The x-intercept is the point (4.67, 0). Another easy point to find and build the graph can be the y-intercept, which is given when x = 0. Replacing in the equation:

`\begin{gathered} 1.5x-3y=7\to x=0 \\ 1.5\cdot(0)-3y=7 \\ -3y=7 \\ y=(-7)/(3) \\ y\approx-2.33 \end{gathered}`

With this, the other point we can use to graph the equation is (0, -2.33).

Drawing both points on a cartesian plane:

Both points (x and y-intercepts) are drawn in red.