I'm unsure how to solve this... can someone help me?
Match the equation with its graph.
−6/7 x - 1/2 y = 3/7
The answers are graphs, so I'll type the coordinates of the graphs here.
A.) -1, 4; -6, 4
B.) -1, -4; 4, 6
C.)-4, -6; 4, 8
D.) -4, 6; 2, -4
are you from connections Abigail?
To match the equation with its graph, you can start by rearranging the equation into slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept. So let's solve the given equation:
-6/7x - 1/2y = 3/7
To isolate the y-term, we need to move the -6/7x to the other side:
-1/2y = 6/7x + 3/7
Next, multiply the entire equation by -2 to get rid of the fraction:
y = -12/7x - 6/7
Now that the equation is in slope-intercept form, we can compare it to the given graphs by matching the slope and y-intercept. The slope (-12/7) tells us that for every 7 units we move to the right on the x-axis, we go down 12 units on the y-axis. And the y-intercept (-6/7) tells us that the line crosses the y-axis at y = -6/7.
Now let's examine the answer choices:
A.) (-1, 4); (-6, 4)
B.) (-1, -4); (4, 6)
C.) (-4, -6); (4, 8)
D.) (-4, 6); (2, -4)
To determine the correct graph, we need to check if the corresponding points on the graph satisfy the given equation. Substituting the points from each answer choice into the equation, we can determine if they make the equation true. Let's do that:
A.) Substitute (-1, 4):
4 = -12/7(-1) - 6/7
4 = 12/7 - 6/7
4 = 6/7
Since 4 does not equal 6/7, this is not the correct graph. We can do the same process with the other answer choices until we find the correct graph that satisfies the equation.
first of all let's clean up the equation
multiply each term by 14 , the LCD
-12x - 7y = 6 , or even nicer..
12x + 7y = -6
slope = -12/7 , which leans to the left
ruling out A, B, and C.
A is horizontal and B and C have positive slopes
this leaves D
I will leave it up to you to test if (-4,6) and (2,-4) satisfy my simplified equation