Question Put the following equation of a line into slope-intercept form, simplifying all fractions. \[ 10 x+8 y=72 \] Answer Attempt 10 out of 2

To put the equation \( 10x + 8y = 72 \) into slope-intercept form (\( y = mx + b \)), we need to solve for \( y \). Start by isolating \( y \): 1. Subtract \( 10x \) from both sides: \[ 8y = -10x + 72 \] 2. Divide every term by \( 8 \) to solve for \( y \): \[ y = -\frac{10}{8}x + \frac{72}{8} \] Simplifying gives us: \[ y = -\frac{5}{4}x + 9 \] So, the slope-intercept form of the equation is \( y = -\frac{5}{4}x + 9 \). Here you go with some fun facts! Did you know that the slope of a line represents its steepness and direction? A positive slope goes upward to the right, while a negative slope, like the one we found (-5/4), goes downward! Slope-intercept form is super handy in real-life applications, like predicting trends in data. For example, if you're looking at how the temperature changes throughout the day, you can model that change using a line. The slope gives you the rate of temperature increase or decrease, while the y-intercept indicates the temperature at a specific time!