Slope-Intercept Form Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. An upward slanting line is graphed on the coordinate plane. The upward slanting line passes through closed points plotted at left parenthesis 0 comma negative 10 right parenthesis and left parenthesis 1 comma negative 7 right parenthesis.
Is this the correct graph of 3x−y=10?
To determine if the graph is correct for the equation 3x - y = 10, we need to rearrange the equation to slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we isolate y by subtracting 3x from both sides of the equation:
-y = -3x + 10
Next, we multiply both sides by -1 to make y positive:
y = 3x - 10
Now we can compare this equation to the given graph. The equation has a slope of 3, which means the line should be upward-sloping. The y-intercept is -10, which means the line should pass through the point (0, -10).
Looking at the graph, we can see that it is indeed an upward-sloping line passing through the point (0, -10). Therefore, the graph is correct for the equation 3x - y = 10.
Now i want you to choose by options.
A. No, it is not the correct graph because the slope is −3 and the y-intercept is (0, −10).
B. Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).
C. No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10).
D. Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10).
D. Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10).
But isnt the answer 3x - y = 10? so why is that answer -10 explain.
I apologize for the confusion in my previous response. You are correct, the equation is 3x - y = 10.
In this equation, the y-intercept is the value of y when x=0. To find the y-intercept, we set x=0 in the equation and solve for y:
3(0) - y = 10
-y = 10
y = -10
Therefore, the y-intercept is (0, -10), which means the line passes through the point (0, -10).
Given this information, the correct option should be:
C. No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10).
Identify the slope and the y-intercept of the equation 4x−3y=12.(1 point)
Responses
The slope is 4, and the y-intercept is (0, 12).
The slope is 43, and the y-intercept is (0, −4).
The slope is −43, and the y-intercept is (0, 4).
The slope is 43, and the y-intercept is (0, 4).
To identify the slope and y-intercept of the equation 4x - 3y = 12, we need to rearrange the equation to slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we isolate y by subtracting 4x from both sides of the equation:
-3y = -4x + 12
Next, divide both sides by -3 to solve for y:
y = (4/3)x - 4
Therefore, the slope (m) is 4/3.
To find the y-intercept (b), we set x=0 and solve for y:
y = (4/3)(0) - 4
y = -4
Therefore, the y-intercept is (0, -4).
Based on this information, the correct option is:
The slope is 4/3, and the y-intercept is (0, -4).