The equation $3y = 10x - 5$ can be rewritten in different forms to make it easier to work with. Below are some options:

1. Solve for $y$ (Slope-Intercept Form):

Divide through by 3 to isolate $y$:

$y = \frac{10}{3}x - \frac{5}{3}$

This is the slope-intercept form $y = mx + b$, where:

• Slope ($m$) = $\frac{10}{3}$
• Y-intercept ($b$) = $-\frac{5}{3}$

2. Solve for $x$:

Rearrange to isolate $x$:

$x = \frac{3y + 5}{10}$

3. Express in Standard Form (Ax + By = C):

Reorganize terms into standard form:

$-10x + 3y = -5$

or

$10x - 3y = 5$

This is useful for graphing or substitution in systems of equations.

Would you like to explore any specific aspects, such as graphing, intercepts, or solving related problems?

5 Related Questions:

1. What are the intercepts of this equation on a graph?
2. How would the graph of this equation compare to $y = 2x + 1$?
3. What is the equation of a line parallel to this one passing through $(2, 3)$?
4. Can you find the coordinates where this line intersects $y = -x + 4$?
5. How would the equation change if the slope were halved?

Tip:

When converting equations, always keep track of which form you're using (e.g., slope-intercept vs. standard), as each has unique advantages!