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-intercept form of the equation, we need to rearrange it in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Given: 9 + (27/2)x = (-3/2)y
Step 1: Multiply both sides of the equation by -2 to isolate y:
-2[9 + (27/2)x] = (-2)(-3/2)y
-18 - 27x = 3y
Step 2: Divide both sides of the equation by 3 to solve for y:
(-18 - 27x) / 3 = (3y) / 3
-6 - 9x = y
Step 3: Now we have the equation in the slope-intercept form: y = -9x - 6
Therefore, the slope is -9 and the y-intercept is -6. As an ordered pair, the y-intercept is (0, -6).
To determine the slope and y-intercept of the given equation, we need to rewrite it in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's rewrite the equation 9 + 27/2x = -3/2y by isolating y.
9 + 27/2x = -3/2y
Multiplying both sides by -2/3 to isolate y, we get:
(-2/3)(9 + 27/2x) = y
Simplifying the equation, we have:
-6 - 18x = y
Now we can see that the slope (m) is -18 and the y-intercept (b) is -6.
Therefore, the slope is (-18) and the y-intercept is (-6, 0).