Question

Identify the slope and the y-intercept of the line 35x + 7y = 56.

Options:
1. Slope = 7, y-intercept = 35
2. Slope = -7, y-intercept = 56
3. Slope = -5, y-intercept = 8
4. Slope = -5, y-intercept = 5

Answer 1

To find the slope and y-intercept, the equation 35x + 7y = 56 is rearranged to y = -5x + 8, revealing the slope as -5 and the y-intercept as 8.

Step-by-step explanation:

To identify the slope and the y-intercept of the line given by the equation 35x + 7y = 56, we first need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the original equation:

35x + 7y = 56

We isolate y by moving the term containing x to the other side of the equation:

7y = -35x + 56

Next, we divide everything by 7 to solve for y:

y = -5x + 8

Now in slope-intercept form, we can clearly see the slope (m) is -5 and the y-intercept (b) is 8.

Therefore, the correct answer is option 3: Slope = -5, y-intercept = 8.