Question

Find the slope and the \(y\) -intercept (if possible) of the line. $$ 6 x-5 y=15 $$

Short answer

The slope of the line is \(\frac{6}{5}\) and the \(y\)-intercept is -3.

Step-by-step solution

Convert the equation into slope-intercept form

To find the form \(y = mx + c\), the equation is simplified by first isolating \(y\). The equation is given as \(6x - 5y = 15\). This can be rewritten as follows: \[-5y = -6x + 15\]Divide through by -5 to isolate \(y\):\[y = \frac{6}{5}x - \frac{15}{5}\]Thus, the slope-intercept form of the equation is \(y = \frac{6}{5}x - 3\)

Identify the slope

In the slope-intercept form \(y = mx + c\), the coefficient \(m\) in front of \(x\) is the slope. From the obtained equation \(y = \frac{6}{5}x - 3\), the slope of the line is \(\frac{6}{5}\).

Identify the y-intercept

From the obtained equation \(y = \frac{6}{5}x - 3\), the \(y\)-intercept, which corresponds to the constant term \(c\) in the slope-intercept form, is -3. This is the point where the line crosses the y-axis.