Slope-Intercept Form Practice
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Question
What is the slope and the y-intercept of the equation 9+27/2x=−3/2y. Write the y-intercept as an ordered pair.(1 point)
The slope is
. The y-intercept is ( ).
To find the slope and y-intercept of the equation 9+27/2x = −3/2y, we need to rearrange the equation into slope-intercept form, which is y = mx + b.
First, let's isolate y by dividing both sides of the equation by -3/2:
y = (9 + 27/2x) / (-3/2)
Simplifying the expression:
y = (9 + 27/2x) * (-2/3)
y = -2(9 + 27/2x) / 3
y = -18 - (27x / 2)
Now we can identify the slope and y-intercept:
The slope, m, is the coefficient of x in the equation. In this case, it is -27/2.
The y-intercept, b, is the constant term in the equation. In this case, it is -18.
So, the slope is -27/2 and the y-intercept is (-18, 0).
To find the slope and the y-intercept of the equation 9 + (27/2)x = (-3/2)y, we need to rewrite the equation in slope-intercept form, which is in the form: y = mx + b, where m represents the slope and b represents the y-intercept.
Step 1: Multiply both sides of the equation by -2/3 to isolate y:
(-2/3)(9 + (27/2)x) = (-2/3)(-3/2)y
Simplifying:
-6 - 9x = (3/2)y
Step 2: Divide both sides of the equation by (3/2) to solve for y:
(-6 - 9x)/(3/2) = y
Simplifying:
-4 - 6x = y
Now, we can see that the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
The slope is -6, and the y-intercept is (-4, 0).