Write the equation in slope-intercept form and correctly list the slope and y-intercept.
5π₯ β 2π¦ = 12
a) π¦ = ; slope: ; y-intercept:
5
2
π₯ β 6
5
2 β 6
b) π¦ = ; slope: ; y-intercept:
5
2
π₯ β 6 β 6
5
2
c) π¦ =β ; slope: ; y-intercept:
5
2
π₯ β 6 β
5
2 β 6
d) π¦ =β ; slope: ; y-intercept:
5
2
π₯ + 6 β
5
2
6
The correct equation in slope-intercept form is π¦ = 5/2π₯ - 6.
The slope is 5/2 and the y-intercept is -6.
Therefore, the correct answer is:
b) π¦ = 5/2π₯ - 6; slope: 5/2; y-intercept: -6
To write the equation in slope-intercept form, we need to isolate the y variable on one side of the equation:
5π₯ β 2π¦ = 12
First, we'll move the 5π₯ term to the other side of the equation:
β 2π¦ = β5π₯ + 12
Next, divide both sides of the equation by -2 to solve for y:
π¦ = (β5/β2)π₯ + (12/β2)
Simplifying further:
π¦ = 5/2π₯ β 6
Now, we can identify the slope and y-intercept:
Slope = 5/2
Y-intercept = -6
Therefore, the correct answer is:
b) π¦ = 5/2π₯ β 6; slope: 5/2; y-intercept: -6
To write the equation in slope-intercept form (y = mx + b), we need to solve the given equation for y.
Starting with the original equation:
5π₯ β 2π¦ = 12
Step 1: Move the term with 5x to the other side of the equation by subtracting 5x from both sides:
-2π¦ = -5π₯ + 12
Step 2: Divide both sides of the equation by -2 to isolate y:
π¦ = (-5π₯ + 12)/(-2)
Step 3: Simplify the right side of the equation:
π¦ = (5/2)π₯ - 6
Comparing this equation to the slope-intercept form (y = mx + b), we can see that the slope (m) is 5/2 and the y-intercept (b) is -6.
Therefore, the correct answer is:
b) π¦ = (5/2)π₯ - 6; slope: 5/2; y-intercept: -6