# What is the equation of the line the passes through the point (0, 2) and is parallel to 6y=5x-24?

Nov 15, 2016

The equation of the line passing through $\left(0 , 2\right)$ is $6 y = 5 x + 12$.

#### Explanation:

Parallel lines have equal slopes.
The slope of the line $6 y = 5 x - 24 \mathmr{and} y = \frac{5}{6} \cdot x - 4$ is $\frac{5}{6}$

So the slope of the line passing through $\left(0 , 2\right)$ is also $\frac{5}{6}$

The equation of the line passing through $\left(0 , 2\right)$ is $y - 2 = \frac{5}{6} \cdot \left(x - 0\right) \mathmr{and} y - 2 = \frac{5}{6} x \mathmr{and} 6 y - 12 = 5 x \mathmr{and} 6 y = 5 x + 12$ [Ans]

Nov 15, 2016

$y = \frac{5}{6} x + 2$

#### Explanation:

The first thing you should notice is that the point color(red)((0,2)
is a specific point on the line.

The $x$ value = 0, tells us that the point is on the y-axis.

In fact it is $c \text{ } \rightarrow$ the y-intercept.

Parallel lines have the same slope.

$6 y = 5 x - 24$ can be changed to

$y = \textcolor{b l u e}{\frac{5}{6}} x - 4 \text{ } \leftarrow m = \textcolor{b l u e}{\frac{5}{6}}$

The equation of a line can be written in the form $y = \textcolor{b l u e}{m} x + \textcolor{red}{c}$

We have both m and c, substitute them into the equation.

$y = \textcolor{b l u e}{\frac{5}{6}} x + \textcolor{red}{2}$