Question

Write the equation in slope-intercept form. Then graph the equation. $$8 x-4 y+16=0$$

Short answer

The equation in slope-intercept form is \(y = 2x + 4\), where 2 is the slope and 4 is the y-intercept. To graph, start at the point (0,4), then move up two units and one unit to the right, giving us another point at (1,6). Connect these points to form the line that represents the equation.

Step-by-step solution

Convert the given equation into slope-intercept form

To convert the given equation, \(8 x-4 y+16=0\), into slope-intercept form \((y = mx + c)\), we need to isolate 'y'. First, rearrange the equation to give: \[ 4y = 8x + 16 \] Divide each term by 4, to find \(y\): \[ y = 2x + 4 \]

Identify the slope and y-intercept

In our slope-intercept equation \(y = 2x + 4\), the slope 'm' is 2 and the y-intercept 'c' is 4. This means the line of the graph goes up by 2 for every 1 move to the right, and it intersects the y-axis at the point (0,4).

Graphing

For graphing, firstly, put a point on y-axis at (0,4), this is the y-intercept. Then, from this point, move 2 units up and one unit to the right, this gives us a second point at (1, 6). Continue this pattern to find a third point. Connect these points with a line and extend it in both directions. This line is the graph of the equation. Make sure to label your axis, the y-intercept and slope.