Final answer:
To express (6x - 4y = 24) in slope-intercept form ((y = mx + b)), we isolate (y). After rearranging terms, the final form is (y = -frac{3}{2}x + 6), representing the relationship with a slope of (-frac{3}{2}) and y-intercept of 6.
Step-by-step explanation:
To write the equation 6x−4y=24 in slope-intercept form, which is y = mx + b, we need to solve for y. The process involves isolating y on one side of the equation. Step 1: Subtract 6x from both sides of the equation: 6x - 4y − 6x = 24 − 6x, −4y = −6x + 24. Step 2: Divide everything by −4 to solve for y: −4y / −4 = (−6x + 24) / −4, y = (−6/4)x + (24/4), y = −3/2x + 6. Therefore, the equation in slope-intercept form is y = −3/2x + 6, where the slope is −3/2 and the intercept is 6.