Final answer:
To rewrite the equation -6x + 5y = 9 in slope-intercept form, solve for y to get y = 1.2x + 1.8. The slope is 1.2, and the y-intercept is 1.8, where the line crosses the y-axis at (0, 1.8).
Step-by-step explanation:
To rewrite a linear equation in slope-intercept form, one must solve for y in terms of x. The standard form of a linear equation is Ax + By = C. To rewrite this into slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept, we manipulate the equation such that y is isolated on one side.
Let's take the given linear equation -6x + 5y = 9 and rewrite it in slope-intercept form:
Add 6x to both sides to get 5y = 6x + 9.
Divide every term by 5 to isolate y, getting y = ⅖x + ⅙5 or y = 1.2x + 1.8 when in decimal form.
The slope (m) of the equation is the coefficient of x, which is 1.2, indicating that for every 1 unit increase in x, y increases by 1.2 units. The y-intercept (b) is 1.8, indicating that the line crosses the y-axis at the point (0, 1.8).