Final answer:
To convert linear equations into the slope-intercept form, rearrange each equation to solve for y. This identifies the slope, m, as the coefficient of x, and the y-intercept, b, as the constant term after isolating y.
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept. To find the slope and y-intercept for each equation, we need to rearrange the equations into this form.
- a. Starting with 5x + 4y = 20, solve for y to get y = -5/4x + 5. Here, the slope m is -5/4 and the y-intercept b is 5.
- b. For 4x + 14y = 28, rearrange to get y = -2/7x + 2. The slope m is -2/7 and the y-intercept b is 2.
- c. With 12x - 9y = 45, rearrange to find y = 4/3x - 5. Here, the slope m is 4/3 and the y-intercept b is -5.
- d. For -5x + 15y = -60, y can be expressed as y = 1/3x - 4. Thus, the slope m is 1/3 and the y-intercept b is -4.
- e. In 3y + 2x = -15, y is y = -2/3x - 5. Therefore, the slope m is -2/3 and the y-intercept b is -5.