I am having trouble with the following : find the slope and the y intercept of the line 7x=6y+12. I have the slope as 3 and the y intercept (0,3)
To find the slope and the y-intercept of the line 7x = 6y + 12, we can rewrite the equation in the slope-intercept form, which is y = mx + b. Here's how to do it:
Step 1: Start with the given equation: 7x = 6y + 12.
Step 2: Solve the equation for y by isolating it on one side. Subtract 12 from both sides:
7x - 12 = 6y.
Step 3: Divide both sides by 6 to get y by itself:
(7x - 12)/6 = y.
Step 4: Simplify the expression on the right side:
y = (7/6)x - 2.
Now that we've rewritten the equation in slope-intercept form, we can determine the slope and the y-intercept.
The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
From the equation y = (7/6)x - 2, we can see that the slope, m, is 7/6. This means that for every unit increase in x, y increases by 7/6 units.
To find the y-intercept, we look at the equation when x = 0. Substituting x = 0 into the equation y = (7/6)x - 2, we get:
y = (7/6)(0) - 2 = -2.
So, the y-intercept is -2. This means the line intersects the y-axis at the point (0, -2).
Therefore, the correct slope is 7/6, and the correct y-intercept is (0, -2).