Step-by-step explanation:
Given equation: -3x + 2y = -4
Add 3x to both sides of the equation:
-3x + 2y + 3x = -4 + 3x
2y = 3x - 4
Divide both sides by 2 to solve for y:
[tex]\frac{2y}{2} = \frac{3x - 4}{2}[/tex]
[tex]y = \frac{3}{2}x - 2[/tex] (This is the linear equation in slope-intercept form).
To graph, we could determine the y-intercept of the equation. The y-intercept is the value of y when x = 0.
Plug in x = 0 into the equation:
[tex]y = \frac{3}{2}x - 2[/tex]
[tex]y = \frac{3}{2}(0) - 2[/tex]
y = - 2
Therefore, the y-intercept is (0, -2).
Now, we can plot the points on the graph using the slope, [tex]m = \frac{3}{2} = \frac{rise}{run}[/tex]. Start by plotting the y-intercept onto the graph, then you can plot the next graph by going 3 units up and 2 units to the right. Keep repeating the steps until you form a line. Please see the plotted points in the attached image.
