Questions: Find the slope and y-intercept for the following equation by writing it in the form y=mx+b. Then graph the equation. -4x+3y=12

Solution Steps

The given equation is $-4x + 3y = 12$. To convert this to slope-intercept form ($y = mx + b$), isolate $y$.

First, add $4x$ to both sides of the equation: $3y = 4x + 12$

Next, divide both sides by $3$: $y = \frac{4}{3}x + \frac{12}{3}$ $y = \frac{4}{3}x + 4$

The equation is now in slope-intercept form, where $m$ represents the slope and $b$ represents the y-intercept.

In the equation $y = \frac{4}{3}x + 4$:

• Slope ($m$) = $\frac{4}{3}$
• y-intercept ($b$) = $4$

To graph the equation, start by plotting the y-intercept, which is the point (0, 4).

From the y-intercept (0,4), use the slope $\frac{4}{3}$ to find another point on the line. A slope of $\frac{4}{3}$ means rise 4 units and run 3 units to the right. This gives the second point (3, 8).

Plot the two points (0, 4) and (3, 8) on the graph, and draw a straight line passing through both points.

Final Answer: