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
a) π¦ = 5/2π₯ β 6; slope: 5/2; y-intercept: -6
b) π¦ = (5/2)π₯ β 6; slope: 5/2; y-intercept: -6
c) π¦ = -5/2π₯ + 6; slope: -5/2; y-intercept: 6
d) π¦ = -5/2π₯ - 6; slope: -5/2; y-intercept: -6
To write the equation in slope-intercept form, we need to solve for y.
Given equation: 5π₯ β 2π¦ = 12
To isolate y, we need to move the term containing y to the other side of the equation.
-2π¦ = -5π₯ + 12
Now, divide the entire equation by -2 to solve for y.
π¦ = 5/2π₯ - 6
Now the equation is in slope-intercept form (π¦ = ππ₯ + π), where the slope (π) is 5/2 and the y-intercept (π) is -6.
Therefore, the correct answer is:
a) π¦ = 5/2π₯ - 6; slope: 5/2; y-intercept: -6
To write the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, you need to isolate y on one side of the equation.
Given the equation: 5π₯ β 2π¦ = 12
Step 1: Move the term with the π¦ variable to the other side by subtracting 5π₯ from both sides:
-2π¦ = -5π₯ + 12
Step 2: Divide the entire equation by -2 to solve for π¦:
π¦ = (-5π₯ + 12) / -2
Now, let's simplify the equation and identify the slope and y-intercept.
a) π¦ = (5/2)π₯ - 6
The slope is 5/2 and the y-intercept is -6.
b) π¦ = (5/2)π₯ - 6/2
The equation is not simplified correctly. The slope is still 5/2, but the y-intercept is -3, not -6.
c) π¦ = - (5/2)π₯ + 6
The slope is -5/2 and the y-intercept is 6.
d) π¦ = - (5/2)π₯ - 6
The slope is -5/2 and the y-intercept is -6.