15. Which graph matches the linear equation: −2x+3y=−6%0D%0A−%0D%0A2%0D%0A%0D%0A+%0D%0A3%0D%0A%0D%0A=%0D%0A−%0D%0A6%0D%0A(1 point)%0D%0AResponses
I'm sorry, but there seems to be an issue with the way you've provided the linear equation. Can you please rephrase the equation or provide more information?
To determine which graph matches the linear equation -2x + 3y = -6, we need to rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Starting with the given equation:
-2x + 3y = -6
First, isolate the y term:
3y = 2x - 6
Next, divide both sides by 3:
y = (2/3)x - 2
Now we can identify the slope and y-intercept:
The slope (m) is 2/3.
The y-intercept (b) is -2.
Using this information, we can determine that the graph matching the equation -2x + 3y = -6 is the one with a slope of 2/3 and a y-intercept of -2.
To determine which graph matches the linear equation, −2x + 3y = −6, we can solve the equation for y and then graph the resulting line.
Step 1: Solve the equation for y:
−2x + 3y = −6
3y = 2x - 6
y = (2/3)x - 2
Step 2: Now, we have the equation in slope-intercept form (y = mx + b), where m is the slope (2/3) and b is the y-intercept (-2).
Step 3: To graph the line, we can use the slope-intercept form. First, plot the y-intercept at (0,-2). From there, use the slope to find other points on the line.
To find another point, we can use the slope (2/3). The slope tells us that for every 3 units we move to the right, we need to move 2 units up. So, starting from (0,-2), we can move 3 units to the right to (3, ?). To find the y-coordinate at x=3, we can substitute x = 3 into the equation:
y = (2/3)x - 2
y = (2/3)(3) - 2
y = 2 - 2
y = 0
So, the point (3,0) is on the line.
Step 4: Plot the points (0,-2) and (3,0) and draw a straight line connecting them.
Now, compare the graph of the line y = (2/3)x - 2 with the given options to identify the one that matches the equation.