Question

Write the equation in slope-intercept form. Then graph the equation. $$ x-2 y+4=2 $$

Short answer

The equation, in slope-intercept form, is \(y = 0.5x + 1\). The line graph passes through the point (0,1) on the y-axis and has a slope of 0.5.

Step-by-step solution

Convert to slope-intercept form

First, rearrange the equation to slope-intercept form (y = mx + b). Starting with the given equation: \(x - 2y + 4 = 2\). We first move x and the constant (in this case 4) to the other side by subtracting them from both sides. This gives us: \(-2y = -x + 2 - 4\). Next, simplify the right hand side to get \( -2y = -x -2 \). Finally, divide each term in the equation by -2 to solve for y. This results in: \(y = 0.5x + 1\).

Determine the values of m (slope) and b (y-intercept)

From the slope-intercept form, we can see that the coefficient of x is m (the slope of the line), here m = 0.5. The constant term is b (the y-intercept), here b=1.

Graph the equation

The y-intercept is the point where the line crosses the y-axis, so start by placing a point at y = 1 on the y-axis. The meaning of the slope = 0.5 is that for each step to the right along the x-axis, go half a step up on the y-axis. Plot several points using this idea and then draw a line that passes through all of them. This line represents the equation.